I bought the 883 last year on close out. Cost me about $2600 with the eyepiece included. I considered the 773 as it was about $700 less expensive.
The differences really come down to the lenses. There's more color fringing/chromatic aberration (purple or cyan edges on objects at distance) with the 773. That being said both are absolutely great and arguably as good or better than anything the European alpha companies have. If you look through both at extended distances on a day with more humidity then you'll readily see the differences. There's really no way around this but to use better optics. The 883 was surprisingly lighter than I expected but I'm used to really heavy telephoto lenses.
The differences really come down to the lenses. There's more color fringing/chromatic aberration (purple or cyan edges on objects at distance) with the 773. That being said both are absolutely great and arguably as good or better than anything the European alpha companies have. If you look through both at extended distances on a day with more humidity then you'll readily see the differences. There's really no way around this but to use better optics. The 883 was surprisingly lighter than I expected but I'm used to really heavy telephoto lenses.