I voted for the big 3; lets face it, it's the only rivalry that matters.
Obviously, the score isn't what we care about regarding rivalries (or we'd compare them all to 1.206), so the clear choice is the big 3.
If we decided to look at rivalries between the best players in the world (the highest known scores at the time), Then the Billy/Steve rivalry was actually the only time you had a battle between the two highest scoring players on the game (Dean broke the highest arcade score in 2009, and has yet to have his "current pb" topped (or taken away from him) at any time in the last 7 years).
So what?
It doesn't seem fair to exclude him from these rivalry discussions simply because no else was (or had been) on his level at the time; IMO a rivalry for the best has to involve the best, so it's either Billy v. Steve, or we just go with the true rivalry and stick to the big 3
EDIT:
EDIT EDIT: Or, we call it the greatest arcade rivaly
EDIT EDIT EDIT: ^ and then it's obviously Robbie and Wes based on the associated skill sets for the higher scores.