I don't know the exact speeds to expect on an AT&T MVNO, but my understanding is that while your phone will show the H+ symbol, the actual data transfer throughput is throttled by AT&T to 3G-equivalent speeds. It will certainly be plenty faster than EDGE though.
In the real world ATT going back and forth between 3G and 4G makes for more battery drain than the Verizon. I was down to 10% by 6 pm in NYC with ATT and at 30% with Verizon. The difference is remarkable in the real world. Verizon wins on real life time regardless of the talk time if ATT is constantly going between 4G and 3G. Web and talk is a real plus on the ATT.
But "best" carrier for this smartphone in my book is very clear. Verizon.
There is no going back and forth between 3G and "4G" on AT&T. ATT's 3g and 4g is the exact same thing for this particular phone.