How you do in the games makes no difference, just your final MMR at the end of things.
Similarly, your end of season rank doesn't actually matter much (apart from duo restrictions), and it's your MMR at end of season that matters.
It's quite possible (and perhaps even probable) that despite having the same rank, you had decidely different MMRs.
If either of you played during preseason, that would also have some impact on where you ended up.
(This probably won't make a significant difference, but there is some minor fluctuation in MMRs due to matchmaking not alwys matching with equal MMR'd people [which in fact is quite rare], so if by random chance someone got matched with people slightly higher than them in MMR, they'd stand to gain more MMR for their wins, so might place very slightly higher by random chance despite the same W/L record.)