4e works a charm for that.

You could use Crushed Metal, if by 'fantasy' you mean 'fantasies of giant robots beating the cogs from each other.'

We're shooting for cheaper and easier than 4e, not to mention something with less prep time. Most of the people who would be doing this are wargamers, as not very many of the rpg crowd at the store do their own minis, so almost no one will have the book on their own.

The idea is to keep it simple, but still feel their character is an individual.

It'd be a mass battle, not one on one.

We might improvise based off of super dungeon explore, if I don't see anything good on rpgnow.

My first thought would be GURPS 4th since it's well balanced, point based, generic (it will work for a whole lot more than fantasy), and the combat system in conjunction with the martial arts supplement makes for some of the best detailed melee combat rules ever in my opinion. However, I noticed that you're looking for something cheaper than 4e (I don't know the price of 4e D&D, but with Martial Arts I suspect that GURPS 4th edition is likely more expensive), and quicker to set up (I would say the two are comparable assuming that the players have good knowledge of the ruleset, but that's unlikely to be the case unless they've already played GURPS 4th in the past). Also, to the get some of the crunchier bits out of the GURPS combat system you'll need to overlay a hex grid onto your combat map, which may or may not be practical. In the past I've done a couple of "gladiator" type pickup games with GURPS that are similar to what you describe and it was a real blast. Very tactically oriented and required a lot of thought to get an advantage against a well built opponent. Probably not for your particular situation, but worth a look if you're ever interested in something more detailed.

Not "generic" per se, but you might find the rules for Mordheim useful, if only as a jumping off point. The combat is tight and if you're clever I don't suspect it would take much to come up with some point values for the various attributes. Or, if you're willing to drop the point buy requisite, just use the stat blocks already presented in the rule books and give everyone a little bit of gold to spend on kit. With the later method you're likely to run into balance issues since some races are more keyed toward melee than others. However, I'd wager that can be solved with carefully done, racially specific, equipment lists and money allowances.

There's also the SJGames Man to Man rules which, as I understand, are the precursor to the GURPS rules. I've never played them myself, but I've heard good things. Very cheap and downloadable in .pdf format from SJGame's digital distribution site, e23.