We can do a Time-Trial form of a competition, where it is open to anyone. A track is selected, and if possible a vehicle class is also designated (either form Single Player or Dirt Tour). You have a set amount of days (like maybe 1 week, 2weeks, or a month) to submit a record. Include the car you picked, the time you set. The plus side to this is that you got no lag to blame, you don't have to add other people and meet up all the time.
Or we can do races in large groups... or go with a double elimination bracket...
One problem that will definitely arise is the possible chance PC players do outside mods and hacks to gain an unfair advantage (i.e. increasing vehicle's acceleration, top speed, grip, etc), so maybe the competition can still be held, but categorized so that only ps3 players face each other, and PC players face each other...
Always remember to have proof ready should you be asked.