Reciver/Integrated same sound?

Only the company can tell you that. Usually the more you stuff into one box, the more compromises have to be made...
Price can tell you a lot.

I just naturally assume that all other things being equal, stuffing a tuner or a HT processor in the same box will be a compromising attribute.

You'll need a bigger power supply to service the additional load, or you'll keep the same power supply but shared system wide. The circuit will become more complex to accommodate more functions, etc.

But you know, your mileage I expect may vary.

obviously, merely being made by the same maufacturer won't cause the integrated and receiver to sound identical (any more than a lexus will perform like a scion). assuming the integrated and amp have identical power supplies, transformers and other guts, they should sound very close. i've owned both the nad 3020 integrated and its receiver version, the 7020 and couldn't hear any difference; likewise a yamaha rx-1000u receiver and supposedly identically-built cx integrated. however, as stated above, in the usual case receiver manufacturers are forced to make cost or design compromises to jam extra stuff into the box; likewise the extra circuitry and functions can compromise sound quality. none of which means that an integrated will always outperform a well-designed receiver.