Please read Shiva Maha Puran on the Lingodhbhava Swami. There it is depicted Shiva as the great God. Both are correct. They are great Gods and to differentiate between them is pure absurdity. Vishnu as Ananthapadmanabha worships Shiva. If he has to keep his dearest devotee, why to keep a Shiva Linga on top of his head while lying down, stretching his hand to it with reverence?