Last November I gave serious consideration to both phones. Hardware wise, they seem pretty equal. Screen aside, I don't think there is much difference between them except for the Razr having a 1.2GHz CPU while the Bionic has a 1.0GHz.
The screen is the most obvious difference. As others have said, some have a preference on to the other, but I really like the Bionics myself.
While I was doing comparisons, the main issue for me was the battery. The Razr has a sealed battery compartment. If you are a light user this may not make a difference to you. But if you think you may have days where you will be using it a lot, and you may not have access or time to put it on a wall or car charger, this can be a big deal. Sure, you can buy one of those bulky external batteries, but they aren't really convenient to carry around or plug your phone into unless your sitting down for some time. At least with the Bionic you can carry a spare battery and change it out quickly.
Honestly, it comes down to personal preference and no one can tell you what to prefer and only you can know what is and isn't the right choice for you, but these are a few of the things I can think of to consider.