There are three different but overlapping reasons for restricting a card in Vintage.
Its power in one specific strategy is such that it would make that strategy unstoppable in the metagame. This is the classic and usual justification for restricting or banning cards, though true examples are rarer in Vintage than in other formats -- perhaps the recently-added Lodestone Golem will serve as a concrete example.
The card unacceptably increases the variances of the format as a whole, without benefiting any specific strategy. Consider Black Lotus, for instance; certainly unrestricting Lotus would benefit some decks (e.g. combo) more than others, but the lowest-order result of unrestricting Lotus would be a much faster format, without ensuring the dominance of any one particular strategy. Now I'm certainly not a fan of a turn-0 format, where success hinges largely on the die roll; on the other hand, I view this justification with a dose of a suspicion. Vintage is all about the broken, early-game plays; who is to say that this amount of variance in Vintage is OK, but that amount is now over the line? It's all very fuzzy and subjective to me.
The card doesn't dramatically increase variance or stunt the metagame, but simply leads to an unfun play experience. This was large part of the justification for restricting both Trinisphere and Chalice of the Void. This criterion is of course incredibly subjective -- the card is unfun according to whom?
My personal philosophy on the restricted list is that the composition of the list should be as conservative as possible. I understand the people saying, "Vintage isn't broken, why fix it?" but would prefer a policy that is as close as possible to the format's stated goal of allowing players to play with all of their cards.
My list therefore would be:
Lion's Eye Diamond
Wheel of Fortune
Unbanned and restricted:
Unerratad and restricted: