Welcome!! I think both of those bikes would be a great ride. Two factors that I would consider is, most importantly the ride, but also important is the support you would receive from the shop you buy from. My local Trek dealer offers lifetime adjustments with new bike purchases-- which as a newbie-- I've used on many occasions!!
Outside of ride and support from your dealer, I'd get the most bike you can afford. If you go Trek and can swing it, consider going up to the 7.3 (or even 7.5) and Specialized, consider going with the Vita Sport (or even Elite) as you'll get a carbon fork on the FX 7.5 and Vita Elite and would really do a lot for your ride quality.
Shannon