I have both an iPhone 4 and an Evo 4G.
I've been through 4 Evo's to get one that worked properly/didn't have build issues (not minor stuff, things like the screen separating from the phone). If I didn't need one for Android development, I'd have given up after the 2nd one.
Your specific questions:
The Evo is fast enough. It's not iPhone 4 fast/smooth, nor is it as quick as, say, the Epic (though the Epic has so many issues right now don't even bother, I tried one for the last week and a half while waiting for my most recent Evo replacement).
Screen quality ... the resolution is fine, but the colors are rather washed out and if you turn the brightness up over half it eats battery like it's going out of style (10 minutes browsing on WiFi ate 8% of the battery). Compared to the iPhone 4's screen it's average at best.
Battery life on the Evo is comical. I run a whole day with my iPhone 4 as my primary phone, 2-3 hours of calls, BlueTooth, WiFi, GPS and Push on ALL the time (if I had to keep turning them on and off to get through a day I'd ditch the thing and get a dumb phone and an iPod Touch), copious email and browsing.
If I tried that on the Evo I'd be out of power by noon. You'll either need spare batteries, one of the extended packs, and to be dilligent about turning features on and off when you're not using them to get better than that.
As a phone it's "okay". It's still missing, even with Android 2.2 some basic features that I've taken for granted on phones (smart or dumb) for years though.
...
Beyond that it's a bit of a spazmodic experience (true for Android in general).
I love the HotSpot feature now that I have a unit which will do it properly, and that now works well enough that I can ditch my Overdrive.
Apps are generally noticeably rougher than on the iPhone, but most of the critical stuff is there. Games are lacking still, and particularly on the Evo you'll run into a capped framerate issue which affects the smoothness/responsiveness.
There's lots of silly non-attention to detail stuff like, oh, if you take a video and then want to MMS it to someone you can't without third party apps unless you chose to use MMS resolution when you first recorded it.
The 8MP camera yields noticeably lower quality images than the 5MP unit on the iPhone (more pronounced with HDR now). Though white-balance control IS nice on the thing.
Video is poor, plain and simple.
There is no way that I could use the Evo 4G as my primary phone right now. If I didn't need a wireless hotspot AND an Android device to test on, I wouldn't have the Evo at all.