The AT&T-branded Lumia 1520 does not have Qi; I don't know if they still have the 32GB model.
The AT&T retail price is $585. The 20-month AT&T Next agreement is $30/mo for 20 months (i.e., $600), although you can buy for just 12 months' worth ($360) and get the rest waived if you buy into another Next contract and turn in the phone in very good condition. If you sign a 2-year agreement, you'll pay $240 up front ($200 for the phone and $40 to setup or extend a contract) and an extra $15/mo for the phone -- that's $600, too.
The Lumia 1520.3 at B&H Photo is $490, has 32GB, Qi charging, and a U.S. warranty. However, repairs will be via a mail-in since you can't stop by an AT&T store. The B&H purchase will likely be sales tax free, so that might save another $30-40 on the cost when purchased from AT&T.
So, the difference between the cheapest AT&T option (Next 12 with the trade-in of your 1520 in very good condition at the earliest possible time) would save $130 off of the 1520.3 price. The Next agreement remains a good deal 3-4 months, depending on sales tax offsets (i.e., months 13-17 of your agreement); after that, it costs more than the 1520.3. All other AT&T options cost more than the 1520.3.
So, if you swing the $490 up-front cost and really want Qi and the full 32GB, the 1520.3 is a good option, particularly if you want lots of freedom about when to upgrade or if you plan to keep the 1520.3 for 18 months or more. If you can live with the AT&T model, take very good care of your phones, and want to upgrade often, a Next agreement is the best plan for a 13-17 month ownership window.
[This part was added 90 minutes later.]
I forgot to mention that the time window for when AT&T Next program is financially advantageous changes if you plan to see a used 1520.3 when you're ready to upgrade. For every $30 you can get, you can cut a month off of the 13-17 month window. Indeed, if you can more than $130 for a year-old 1520.3, the Next program is never a better deal in terms of cost. However, if the $490 up-front cost is a problem for you, the resale value of the 1520.3 is irrelevant because this option isn't available to you.