My husband has a Bionic and I have a Razor, so we compare them all the time. If I had to pick between the two, I'd probably choose the Bionic. I'm not sure if it's just my phone or if it's a common issue with the model, but my Razor has horrible problems with dropping the data connection. We will be sitting side by side and he will have a great 4G connection and I will have nothing. I use a lot of data-sucking apps and this is a huge sticking point for me. I lose my connection multiple times a day. Today is my first day on ICS on the Razor, so I'm hoping that it will be better.
As for his Bionic, I will say that he has had to have it replaced it 3 times. Once because he had it with him on his motorcycle and got caught in a downpour (the 3rd day after it came out), once because it just seemed to stop working, and most recently because any time he would set it down on a table surface, the force of being dropped (and by dropped, I just mean how you would normally put your phone on a table) to the surface would trigger the phone to shut down.
One thing I've loved about my Razor is how tough it is. I have a screen protector on it, but no case. It's got some dings and scratches on the corners, but it's survived some pretty dramatic falls.
I originally picked the Razor because I wanted the bigger screen. Because the phone is so wide and thin, it's hard for me to hold it securely in one hand and type with my thumb like I would like to do. The Bionic is a better size for me.