As near as I can tell, the stats displayed are pretty much irrelevant, and whether you win or lose is just completely random. (and, additionally, as your stats get better, the stats of your potential opponents get better, faster, so it's not long before it's hard to find an opponents with lower stats... not that it seems to matter much).
i.e. the PvP is a scam to, I guess, try to get you to spend to upgrade. Except it doesn't seem like there is actually any point to upgrading.