What category of living entity is Lord Siva?

Srila Prabhupada - "Lord Śiva is not one of the living entities (Siva is NOT a jiva-tattva (jiva-soul) or Visnu-tattva (Krsna's direct expansion)

Siva is in a league of his own, although he is simultaneously more or less, Kṛṣṇa Himself also (a paradox). 

The example of milk and yogurt is often given in this regard, yogurt is a preparation of milk, but still yogurt cannot be used as milk. 

Lord Śiva is an expansion of Kṛṣṇa, but he cannot act as Kṛṣṇa, nor can we derive the spiritual restoration from Lord Śiva that we derive only from Kṛṣṇa. 

Lord Siva is simultaneously one with and different from the viṣṇu-tattva. Due to Siva's association with māyā, he is different from the viṣṇu-tattva, but at the same time he is an expansion of Kṛṣṇa's personal form. This situation is called 

bhedābheda-tattva or acintya-bhedābheda-tattva, which means- 

"Simultaneously one and different."

The essential difference between Siva and Krsna and Viṣṇu is that Lord Śiva has a connection with material nature, but Viṣṇu or Lord Kṛṣṇa has nothing to do with material nature."(From The Teachings of Lord Caitanya, Ch 8 and CC Madhya 20.308, Purport)

Srila Prabhupada - "The word śiva means "all auspicious." No one can be an enemy of Lord Śiva's, for he is so peaceful and renounced that he does not even construct a house for his residence, but lives underneath a tree, always detached from all worldly things." (SB, Canto 4 Ch 2 text 1, Purport)

Srila Prabhupada - "In Brahma-saṁhitā the example is given of an original candle which lights a second candle. Although both candles are of equal power, one is accepted as the original, and the other is said to be kindled from the original. The Viṣṇu expansion is like the second candle. He is as powerful as Kṛṣṇa, but the original Viṣṇu is Kṛṣṇa. Brahmā and Lord Śiva are obedient servants of the Supreme Lord, and the Supreme Lord as Viṣṇu is an expansion of Kṛṣṇa."(Teachings of Lord Caitanya, Ch 8)

Lord Siva is considered Krsna's greatest devotee.

1 - Lord Siva (Siva-tattva) has 85.938% of Krsna's qualities which means he has 55 of Krsna's 64 qualities. 

2 - The jiva-souls (jiva-tattva)  have 78.125% of Krsna's qualities which means they have 50 of Krsna's 64 qualities. 

3 - The Visnu-tattvas (direct expansions of Kṛṣṇa), on the other hand has 93.75% of Krsna's qualities which means they have 60 of Krsna's 64 qualities.*

Compiled by Gauragopala Dasa Acbsp (initiated by Srila Prabhupada on July 10th 1972).