well, E6600 to E6800 isn't much of an upgrade, especially if you overclock. You see, all of the Core2 chips pretty much come out of the same mold, but some come out better than others,(granted the e6800 comes out of a smaller version of that mold with some small improvements, and the ability to overclock further, but that's relatively minor) they quickly sort them based on quality, then put the number on them and lock the multiplier at whatever speed they see fit. Because of that, if your motherboard can support a high enough FSB speed at it's end, you can pretty much trick the e6600 into thinking it's an e6800 and running at that speed (or even higher). Now, sometimes the quality of the chip isn't that great, and it won't work trying to run as if it was a higher chip, but 45nm has been around for a while and intel has gotten very good at it, so there's a very high chance it will.
Also, while they're clocked lower, the Core2 Quads are basically just a pair of Core2 Duos glued together. Pretty much the only extra risk on the chip side is that one of the chips will stop being able to run any higher long before the other. (as long as you keep the heat in check) On the motherboard side there is the risk that your motherboard might not be able to run it's FSB high enough to max out the chip, or that you might try to draw more power than the motherboard can supply.
My reccomendation if you already have an e6600 is to see how high it can go. If you hit 3.5ghz or so (wasn't that about the safe max for the 65nm intels?) then your computer will probably feel pretty fast again. If i had to guess I'd say that right now you're pretty CPU limited at 2.4ghz. I game at 1080p, and my Kuma is probably the equivalent of your CPU at 2.7ghz, and my 4870 is only a tad faster than the 5770, and I feel like I'm generally CPU limited with all the graphics settings virtually all the way up. (I have shadows one notch below max in WoW, and textures at medium instead of high in SC2 because I have the 512MB 4870)
