The only thing it impacts is your ability to move up to an earlier flight by yourself at a kiosk in the airport, in my experience.

By this I mean, if you don't check in online, when you arrive at the airport and go to a check-in kiosk, if an earlier flight is available, it will typically prompt you with something along the lines of "this other flight is available, would you like to move up to it?" and you can press "yes" and take care of it yourself.

If you check in online, you'll just have to ask the ticket agent behind the counter to process the move up for you. Ultimately, you may save a couple minutes if you don't have to wait and talk to someone, but that's about it.

Ultimately, really no difference at the end of the day.