It would be completely different. Yes, some players play for stats. But players would quite literally only play for stats. Every single one of them. There would be absolutely no incentive to be a team player, to do the little things that teams need to win. Your defensive ends would never ever play run, they'd just be trying to sack the QB every play. Your safeties would gamble on every single play. Your secondary would be giving up huge, huge plays on a constant basis because they'd all be gambling for picks instead of playing fundamental coverage. Quarterbacks would audible out of runs whenever possible. On and on and on. There would be constant locker room issues. There would be constant issues between players and the coaches.
It would be a Tijuana donkey show.