All of the information provided is well and good. But, I ask, what do the two gods represent? The same divine absolute. There are mantras from the vedas that say
Twam brahma, Twam Vishnu, Twam Rudrah, Twam Prajapatihi
It simply means
Thou art Brahma(the paramount), Though art Vishnu(the protector), Thou art Rudra(the destroyer/the exterminator), Thou art Prajapathi(the lord of all/ the creator).
There is another mantra which states
Pranoh Brahma, kam brahma and Kham brahma
which is actually one of the definitions for god, which means Brahma(The supreme divine, not to be confused with the creator, 4 headed Brahma) is actually the vital force within every living entity responsible for evolution(pranoh brahma) the prana is brahma, which is also present in a fluid/water form the 'kam' which represents everything the human mind can perceive and understand and also the things beyond this, everything that is real, the number of points (as in the notion from philosophical math) that exist? the past and the present, the logical, the infinite, the vishnu. Finally, the same devine being exists as 'Kham' the ethereal form, beyond everything the human mind can understand and perceive, reality and beyond, the number of points that exist? and also the superset that includes the points that dont exist at all along with all the points that exist, the intuition, the infinite which is both 0/0 and infinity, the shiva.
In other words, they are the same person, the same god, or there is no shiva, no vishnu, just the supreme parabrahma. The fights are just the illusions created in the minds of people, who couldn't understand the complex working of the universe. The human minds perceived Darwinian theory and Mendel's theory to be counter active, it turned out both are true and complementary. The same goes for Shiva and Vishnu.