I have the Evo Shift & my girlfriend has the Evo. The main difference, as everyone knows, is the keyboard (or lack thereof). If you want a keyboard, go with the Shift. If it's of no concern, stick with the Evo. Also, the Shift is a bit smaller, which is a plus for me (and may or may not be for you). But to answer your questions... the Evo has a 1 GHZ Snapdragon - Adreno GPU while the Shift sports an 800 MHZ Qualcomm processor... I could get technical, but I've read COUNTLESS websites & threads about how the Shift's GPU is far more superior than the Evo's... better gaming. I'm not sure if you plan on keeping stock or OC but personally I think both phones are great for gaming, and if you're power hungry then there is always the option of dual-core!
I also agree that battery life is better. As stated above, I have the Shift and my girlfriend has the Evo. We were together for an entire day one time and basically pulled out our phones at the same times during certain times to check messages, answer a few phone calls, etc... at the end of the day my battery life was almost double hers! Not sure what her settings were but the fact that the Shift has a smaller screen and slower (but still incredibly fast(er) than the Evo's..) processor almost guarantees better battery.
Finally, an important thing to remember is this is the Evo Shift forum, so I can't speak for everyone else but my answer is more biased towards the Shift since I own one! lol. This question would probably be better in a more neutral territory, but if you get the Shift, you will not be disappointed.