Denon AVR-1712 vs. AVR-1713 - Why is the 1713 better?

The advantage of the 1713 is the networking, Airplay, internet radio streaming and USB port.

If you don't need either then get the 1712 which gives you 7.1, Zone 2 and more analog inputs.

Isn't the 1713 also 3d capable whereas the 1712 is not?

The 3D capability was introduced with the XX11 models, so the 1712 is also 3D capable.

Afro GT (or others), is there a Marantz equivalent of Denon 1713? My mandatory needs are ...
5.1 output
3D capabilities
Audessey multeq XT

Nice to have - networking (primarily for firmware upgrade), airplay

I am a bit inclined to Marantz brand - the slimline NR 1403 will probably met some of the needs - but 50W o/p is my major concern; on the other hand SR5007 will probably meet all my needs and more, but that comes with a solid $500 additional price tag. Any suggestion?

The Marantz 5006 and 5007 are the lowest models in the line with XT.

I want to buy a returbed avr 1712 from the Denon Shop. Can anyone tell me if the last firmware update has resolved most basic issues? I don't need networking, but I don't want to have to disconnect the unit and bring it to a dealer in the near future.

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There's no real info available on updates for the non-networking models, so can't answer your question; however, considering that other than the recent Pandora update, the last update received by the networking models was this past summer, it's unlikely there was anything available for the 1712 past that date. Generally the non-networking models don't get firmware updates unless something major needs to be fixed as it takes a special jig for the repair shops to be able to update them and not all repair facilities have access to this jig.