The HTR-7065 over the 573 for sure. 7065 is like the 773 or 775 so you get dual HDMI outputs, more power, 7.1 preouts in case you want to add more power later.
It is two levels above the 573 on the Yamaha product line.
The 573 only has Zone B which is different that Zone 2. With Zone B you can only play the same thing as the main zone. With Zone 2 you listen to one source in the main area and a different source in Zone 2 if you so choose.