Batman's role isn't to keep Superman in check or from going over the edge; Clark trusts Batman to do what's necessary if that does ever happen yes, but they are friends. If anything, their roles are to be aware of the others blindspots; bruce is too cynical, clark is too optimistic so they catch what the other misses.
As far as the movie, the point has been made and rehashed to death so I won't even go into it
And Superman is more tied to the Moses story to me. Not saying the Jesus stuff isn't there but the initial story is so similar to Moses: family sends their son to live with another family to give him a better chance at life and a chance to start over and he's raised with their values and their morals. It BECAME more similar to Jesus as more writers came on and took the reigns but Siegel and Shuster seemed to have Moses more in mind than Jesus..especially being Jewish