Both of these phones are outstanding. Pick the one you like best. The people on this forum who enjoy going back and forth with one another over which phone is better... Seriously? Know what I mean? It's a phone.
I am a high school assistant principal. I once had to deal with a little fight between two freshman who got into it over the brand of athletic socks one of them chose to wear. Razr v. Bionic, Android v. Apple, etc., and all of the similarly stupid "discussions" remind me of kids bickering over trivial crap.
I happen to love my new RAZR and I am sure there are many people who love their Bionic. If the fact that you cannot replace the battery when you're out and not near a charger seems like it might be an issue for you then I'd suggest the Bionic. You can keep a spare battery on you.
The RAZR is really thin, really light, and the display looks fantastic, IMO. But... If you allow the device to automatically dim the screen looks a little dingy, with a slight greenish tint (to my eyes). Disable that feature and turn up the brightness and it looks superb. If you view it from a sharp angle, even with the brightness up, it has a slight blueish cast to it. This is something that will never be an actual issue as, in the real world, you won't be viewing your device from such a crazy angle.
Keyboard app is superb. I am sticking with it instead of using Go.
Animations are smooth. The phone is ridiculously fast. The Bionic is too. If this means anything to you I got a score of 5979 on AnTuTu with my RAZR, a 2804 with Quadrant, and am getting 21.68 Mbps down and 12.14 Mbps up on Ookla Speedtest.net. A Bionic owner can post his/her numbers or you can search for them on this forum. They're similar.
These are both great phones. People who are into this stuff (I count myself in that group) and into sites like this make a big deal out of the tiniest differences or "flaws" in these devices. They're all really amazing, IMO.