Both Rama and Krishna prayed to Lord Shiva in Ramayana and Mahabharata respectively. (Interestingly, the two epics have different authors, and the author of the latter, Sri Ved Vyas, according to Vaishnavites themselves, has also transcribed the Vedas, Puranas, Mahabharata, Srimad Bhagvatam)
In Mahabharata (again by Ved Vyasa), while Bhishma is able to tell Yudhisthira the 1000 names of Lord Vishnu, he is not qualified to do so for Lord Shiva. Only Krishna is able to tell Yudhisthira the 1000 names of Lord Shiva.
In Mahabharata, when Lord Shiva appears before Ashvatthama to answer his prayers, He tells Ashvatthama that He had been protecting the Pandavas at Kurukshtra and so nobody was able to harm them. (But one should also remember that Krishna's cunning is instrumental is providing this safety to the Pandavas.) When aided by Lord Shiva, Ashvatthama murders the Pandavas' sons.
As goes the Gita, Krishna there represents the Brahman (because He is the most Godly among all men gathered on the battlefield, and especially Godly to Arjuna).
The Sudarshan Chakra of Lord Vishnu, his major weapon, was gifted to him by Lord Shiva.
I think it is fair to assume that in Hindu mythology, Lord Shiva is portrayed as the All Powerful (and also All Creative because he is considered the Lord of Arts and Sciences) and Lord Vishnu as the All Cunning, i.e. smart in behavioral matters (neither in bad sense). So, instead of fighting over who is greater, Hindus should accept what the two Gods have to offer and pray to both. In reality you need both faculties to run your life, just as both Gods are needed to run the spiritual sky (irrespective of what the bigots have to say).
In reality, both forms of God are a means to an end.
