Little difference, seriously what has UN done to REALLY affect history. From a military standpoint, nothing really that would not have been done anyway. As for negotiations and treaties and such, at least until the end of the Cold War everything important was between the USA and the USSR. Post Cold War, one side has been blocking almost everything another wanted to do especially in the SC. Iraq was hardly the first time a group of countries ignored the UN and it won't be the last.
Personally I believe that this world would be better without the UN. I'd raze that building and turn it into a parking lot for Downtown NYC (we'll put all our SUV's there). Anyway, I believe that most countries would be allied with other larger countries for protection and that major negotiations would be held simply among different nations multi-laterally. I believe that like the G8/9 is now, you would have organizations like that related to peace, etc.
The only downside I see I can possibly think ya'll see (I don't think it is one) is a situation kind of like the Cold War where most major wars are averted but smaller proxy wars are common. I don't see it as a problem because looking back since the end of the Cold War, the frequency of conflicts and wars have increased dramatically. Hell, America has been in more engagements during the last 14 years then in the previous 30.
As for the upside, America won't have to pay a quarter of the UN's budget, we won't have to deal with small, crackpot regimes who by the blessings of the UN are in change of human rights, and we def won't have to worry about France blocking what we want to do. Some of ya'll would argue that we need that restraint but I believe that the UN is actually stopping things from getting done, maybe now how its done but the fact is military action is the most 'persuasive' diplomatic tool we have and just countries willing to use that tool are held back by the UN which is just a paper tiger.
Melvin, I'll PM you later.