They should sound about the same, except that RX-V1 has a tuner because the A1 is only an integrated amp and the latter is a receiver.
I used to own a Yamaha RX-V2095, which was one notch below the A1. A year later I wanted to upgrade to the AX-1 (same version as the RX-V1, except without the tuner). I A/B tested both the V2095 and AX-1 with the same cd player and speakers at my audio dealer, and found only very minute (and I do mean minute) difference in sound between the two, due mostly to the better amp in AX-1 versus V2095, and not the DSP chip, according to my dealer.
If you really want to spend $1,600, my advice to you is to buy separates, or if you really set on the DSP functions of Yamaha, then buy the A-1 and then add a separate 5 channel amp. Then you will realize how important a decent amp really is in a system, or conversely, how lousy (and I do mean lousy) an amp all receivers have in them......
