The thing is, these tanks are not real. They are balanced by numbers that mean nothing in the real world and are only relevant to performance in the game.
Any unit can be balanced to be however it needs to be, or simply how the dev doing the work wants it to be. Example: OWA wants a nod buggy that beats everything. Well he simply edits the nod buggy to do his bidding and b00m! Buggy of death! It could kill anything in 1 hit if he wanted it to.
The answer to this question lies with what version of each that you pit against each other, as the Soviet mammoth has undergone a few balance overhauls since the beginning of APB, and the GDI one in a mod like IA might not be the same balance-wise as the one from 2003 Renegade. A fun test for sure, but really hard to determine which one is "better" because of the circumstance.
No, they're not. In-game representations have nothing to do with how these units would perform in a real-life scenario. If they existed in real life and faced each other on a real battlefield, the modern GDI Mammoth would almost always beat the now-outdated Soviet one (unless the Soviet crew had some amazing luck or something). Like it or not, 40 years of technological advancement is going to make a difference.
I tend to agree with the "40 years of advancement" view. This is simply logical. The GDI rendition of the mammoth would certainly not be any worse than the Soviet mammoth, even if the design somehow miraculously did not advance whatsoever in 40 years. If this were real, and you had a GDI mammoth tank...assuming that you could find a still-functional GWWII-era Soviet mammoth tank, I'd feel certain that the GDI one would win. If for no other reason than 40+ years of rust on the Soviet one might have a slight impact on performance