AT&T's only clear technical advantage is the ability to use voice and data services simultaneously on the same device. If that is a capability you want/need, get AT&T, as you can't do it with a CDMA phone (Sprint/Verizon).
On the dropped call front, my geekiest friend with an AT&T iPhone says he occasionally suffers dropped calls, but more often is simply unable to place calls on his first try. I've had a Verizon Blackberry for about 5 years and can't remember the last time I had a dropped call outside an elevator, although with my current Blackberry (a Curve2) I have to place calls more than once before they go through sometimes. My previous blackberry, an 8730e, never seemed to have that problem so I don't know if the network got worse around the time I upgraded or if my newer Blackberry just isn't as reliable.
Before I got a Blackberry I had a Sprint dumbphone. It worked okay and was cheaper than Verizon, but there were lots of places in the city I didn't get service--once I switched to VZW I noticed a remarkable improvement. I think Sprint has improved in the last five years, but Verizon still seems to be the leader in terms of coverage. Very, very few businesspeople seem to use Sprint.