When referring to the comparison of two things or people then it's always "on par". I think it's safe to say that "on par" is short for "on par with eachother."
If you're talking about something being or reaching a particular level, getting to certain point, then you want to say that something is "at par".
The phrase "at par" is most commonly heard in golf, explaining that a golfer's score is "at" a certain number, the number that is par. In this case because par is referring to a specific number, you can't really say a number is "on" another number so that's why the preposition used in this is "at".