Srila Prabhupada - "It is to be understood that although all the Vishnu-tattvas, from the original Krishna to Lord Chaitanya, Rama, Narasimha, Varaha, and so on, appear with different features in different ages, all are equally invested with supreme potency" (Adi 3.71, Purport)

Explaining the position of Lord Caitanya Mahaprabhu is a little complicated.

To start with, Krishna NEVER leaves Goloka Vrindavana, therefore when He comes to our Earth, He comes as His Vishnu-tattva expansion and plays the part of Krishna who NEVER leaves the Spiritual World of Goloka-Vrindavan.

Krishna in Goloka-Vrindavan actually never kills demons there because they do not exist there in the Spiritual World. 

Vaikuntha also means "without anxiety".

Only in the the "facsimile Vrindavana on this Earth globe in the material creation" do demons exist and are killed by Vishnu who is playing the role of Krishna here in the material creation.

So we understand that Krishna is the original Form of Godhead, meaning even Lord Caitanya Mahaprabhu in the material creation, being a combination of Srimati Radharani and Krishna, are also Vishnu-tattva expansions of Krishna.

Srila Prabhupada - "In the category of Vishnu-tattva there is no loss of power from one expansion to the next, any more than there is a loss of illumination as one candle kindles another. Thousands may be kindled by an original candle, and all will have the same candle power. In this way it is to be understood that although all the Vishnu-tattvas, from Krishna and Lord Chaitanya to Rama, Narasimha, Varaha, and so on, appear with different features in different ages, all are equally invested with supreme potency. (Chaitanya-charitamrita, Adi 3.71, Purport)

Srila Prabhupada's candle analogy draws on a traditional example found in the Brahma-samhita (5.46), objectively establishing Krishna as supreme among manifestations of the Lord -

Srila Prabhupada - "The light of one candle being communicated to other candles, although it burns separately in them, is the same in its quality. I adore the primeval Lord Govinda [Krishna], who exhibits Himself equally in the same mobile manner in His various manifestations."

Brahma states this even more directly earlier in that same work (5.1) - 

"Krishna, who is known as Govinda, is the Supreme Godhead. He has an eternal blissful spiritual body. He is the ORIGIN of all. He has no other origin, and He is the prime cause of all causes."

And then again (5.39)- 

"I worship Govinda, the primeval Lord, who by His various plenary portions appeared in the world in different forms and incarnations, such as Lord Rama, but who personally appears in His supreme ORIGINAL form as Lord Krishna."

Brahma reiterates this point in the Srimad-Bhagavatam (10.14.14) after seeing Krishna produce innumerable Vishnu forms from His transcendental body. 

Addressing Krishna, Brahma says, 

“Are You not the original Narayana [Vishnu], O supreme controller, since You are the Soul of every embodied being and the eternal witness of all created realms? Indeed, Lord Narayana is Your expansion, and He is called Narayana because He is the generating source of the primeval water of the universe. He is real, not a product of Your illusory Maya.”

So, while full manifestations of Krishna are all equal, there is the fact that one comes first meaning Krishna is the original  Supreme Personality of Godhead. 

In this capacity He is known as avatari—the source of all incarnations—as opposed to avatara. Krishna and His full incarnations are the same Supreme Person in different guises for distinct purposes, ranging from accepting the regal worship of His servitors in the spiritual world to intimate exchanges with His confidential devotees in Vrindavan.

According to Srimad Bhagavatam, the oneness of Krishna's many expansions exists in the realm of "tattva", which means "philosophical truth". 

But there is a higher principle in Vaishnavism, known as rasa, or the ecstatic interactions of the spiritual realm.

It is true that several Vaishnava lines, such as the Sri Sampradaya, see Vishnu, also known as Narayana, is seen as the highest manifestation of God. That is their prerogative.

However, the devotees of Krishna understanding the common identity of Krishna and Vishnu, respect the devotion of Vishnu's devotees. 

When Sri Chaitanya Mahaprabhu met with members of this lineage, for example, He was pleased to see how devoted they were to Vishnu. 

Similarly, in Sanatana Goswami's Brihad-bhagavatamrita (2.4.99–107) we learn that the residents of Vaikuntha, the majestic kingdom of God, prefer Vishnu to Krishna. 

Sanatana Goswami reveals this to be their particular bhava, or emotion, and it is pleasing to Krishna that Narayana's devotees in Vaikuntha see Him in that way.

But those who come in the line of Chaitanya Mahaprabhu, who revealed an esoteric side of the Vaishnava tradition, see Krishna as Supreme Personality of Godhead and cause of all causes, knowing Him to be the original Personality of Godhead and source of all Narayan and Vishnu forms of God. 

While this was certainly the bhava taught by Mahaprabhu, it can also be demonstrated objectively with texts such as the Srimad-Bhagavatam and the Brahma-samhita.

It is the Srimad Bhagavatam that makes the most famous statement about Krishna's primary position -

ete chamsha-kalah pumsah

krishnas tu bhagavan svayam

"All of the above-mentioned incarnations are either plenary portions or portions of the plenary portions of the Lord, but Lord Sri Krishna is the original Personality of Godhead." (Bhag. 1.3.28) 

The First Canto’s Third Chapter proves this point, its first four verses glorify the Vishnus who appear in the beginning of creation, and then it lists a number of important incarnations, including Krishna Himself. It is only at the end of the list that we find the words -

 "krishnas tu bhagavan svayam or Krishna is God Himself"

These words confirm Bhagavatam's statement that Krishna is the Supreme Godhead and cause of all causes.

Srila Prabhupada's commentary on this text is clear - 

Srila Prabhupada - "In this particular stanza Lord Sri Krishna, the Personality of Godhead, is distinguished from other incarnations. According to Srila Jiva Goswami's statement, in accordance with authoritative sources, Lord Krishna is the source of all other incarnations. It is not that Lord Krishna has any source of incarnation."

According to Sri Jiva Goswami, this verse (krishnas tu bhagavan svayam) is the paribhasa-sutra of the entire 18,000-verse Bhagavatam. 

A paribhasa-sutra states the central theme of a literary work. 

In his Krishna-sandarbha (Anuccheda 73), Sri Jiva elaborates, writing that the many verses of the Bhagavatam might be compared to an army, with this verse the monarch who commands that army. He further shows that, according to this verse and many others, Krishna is the original form of God and the ideal object of pure devotional service.

Jayadeva Goswami's Gita Govinda (circa twelth century) also proclaims Lord Krishna's primary position among incarnations, reinforcing the teaching of the Bhagavatam. 

After listing ten prominent incarnations of Vishnu in the book's first chapter, Jayadeva concludes by stating that Krishna is their original source. 

In fact, Jayadeva implies Krishna's preeminence throughout the Gita Govinda and states it explicitly in Act 1, Verse 16 (da śakriti-krite krishnaya tubhyam namah) -

"O Krishna, I offer my obeisances unto You, who assume these ten spiritual forms."

Krishna's Unique Qualities

In the Bhakti rasamrita sindhu, Rupa Goswami lists sixty-four characteristics or qualities exhibited by Krishna. 

Fifty of these attributes can be found in an ordinary soul (jiva-tattva) which is 78.125% of Krishna's 64 qualities that includes Lord Brahma and the demigods in the material creation (except for Shiva who is in a unique league of his own)

Lord Shiva possess fifty-five attributes (84.375% of Krishna's 64 qualities) and is neither jiva-tattva or Vishnu-tattva. 

Vishnu or Narayana displays up to sixty of these attributes (93.75%) out of Krishna's 64 qualities. 

But the remaining "four" are found ONLY in Krishna, and unique to ONLY Him, not found in all other manifestations of the Supreme like Vishnu and Narayana. 

The four qualities unique to Krishna are as follows -

1. Lila-madhurya: He exhibits numerous wonderful pastimes for the pleasure of His devotees.

2. Bhakta-madhurya: He interacts with loving devotees in intimate ways.

3. Venu-madhurya: He plays on His divine flute, thus attracting all souls.

4. Rupa-madhurya: His beautiful form is incomparable, unrivaled in all of existence.

Embedded in these explanations of Krishna's supreme position is something more fundamental: Krishna's supremacy underscores the superiority of love over power, sweetness over opulence.

Bhaktivinoda Thakura writes in the Navadvipa Bhava Taranga (118) - 

"As much as my Sri Krishna is endowed with utmost sweetness [madhurya], similarly the Lord of Vaikuntha is endowed with absolute opulence and grandeur [aishvarya]. Lord Krishna as Vrajendra-nandana [the darling of the king of Vraja] never gives up this same opulence, but such aspects of His spiritual grandeur are considered unimportant by His pure devotees."

In other words, while Krishna sometimes reveals an opulent side that parallels that of Vishnu, as, for instance, when He enacts His kingly pastimes in Dwarka, Vishnu never displays the sweetness associated with Krishna and His associates. 

Therefore, it can be said that Krishna has attributes not found in Vishnu—pastimes of intimate, familiar love.

But keep in mind, Krishna never leaves Goloka Vrindavana and when He comes to the facsimile Vrindavana in the material creation it is Vishnu playing the role of Krishna as painting below reveals.

Krishna never kills demons in the material creation, Vishnu does while playing the role of Krishna.

Most beliefs in God, even in the Vaishnava tradition, naturally evoke awe and reverence, such as in the Vaikuntha Planets with Narayana and Vishnu where the jiva souls have an all in reverence relationship with Vishnu who they know is God. 

However, in Goloka-Vrindavan it is different, no one's sees this young Cow herd boy Krishna as God, He is simply their dear friend who evokes intimacy, friendship, personal reciprocal relationships of loving exchanges and intimacy in Goloka-Vrindavan the top most Spiritual Planet. 

It is this, beyond all else, that distinguishes Him among manifestations of the Supreme. And love, as we all know, is the highest phenomenon in all of existence. 

In conclusion, the Gaudiya Vaishnava vision of the Divine is that all forms of Godhead are equal—since there is only one God—but Krishna enjoys a special position as the "candle who lights the other candles." 

In addition to His ontologically prior position as the source of all Vishnu manifestations of the Supreme, He exudes a sweetness and intimacy that eclipses the power and majesty of other divine forms. 

In fact, His all-attractive nature (Krishna means "the all-attractive one") even attracts other manifestations of the Lord. 

Srila Prabhupada explains that Krishna is known as Madana-mohana because He conquers the mind of Cupid (Madana). When He stands in a three-curved way, He attracts all living entities, including the demigods. Indeed, He even attracts the Narayana form presiding in every Vaikuntha planet.

Srila Prabhupada writes in Chapter Ten of Teachings of Lord Chaitanya-

Srila Prabhupada - "There is no beauty to compare with that of Krishna, who is the origin of Narayana and all other incarnations, for no one possesses beauty equal to or greater than Krishna’s. Otherwise, why would the goddess of fortune, the constant companion of Narayana, give up His association and engage herself in penance to gain the association of Krishna? Such is the superexcellent beauty of Krishna, the everlasting mine of all beauty. It is from that beauty that all other beautiful things emanate."**..