I have both of them activated right now and will be doing some side-by-side comparisons. But my initial impressions are pretty good on the Verizon iPhone. I think all things considered, I'm pretty much torn between them.
Judging by speed tests alone, the AT&T one knocks the socks off of the Verizon one. But in real-world use, it's pretty much a wash. For anything other than video streaming or large file downloads, I really haven't seen much difference in speed between the two.
What I am noticing is that the Verizon iPhone will often start loading a web page more quickly than the AT&T version. But the latter will often finish first. Audio streaming actually starts a bit faster on the Verizon phone, while both of them can keep a steady stream very well. Youtube favors the AT&T app because the faster download will allow a larger portion to buffer and the video will start sooner.
The hotspot feature is awesome, so let's hope it does indeed come to AT&T! And right now, I'm leaning towards the Verizon simply because I can have both Unlimited data and 2GB of tethering on the hotspot. And for the long-term outlook, Verizon will probably have LTE in my area next year before AT&T, so I might be in better shape with next year's iPhone release.
I have yet to see if the Verizon can keep a signal in areas that I've had trouble with on AT&T. For example, in my workplace the AT&T will often drop down to Edge or lose signal altogether when I am trying to stream audio. I will be testing this over the next couple of days to see how the Verizon performs.