I'd go on reviews of the equipment rather than making generalised recommendations.
I'd say that you will certainly get differences in the capability of the power amp to drive difficult speakers, and the quality of the processor and pre-amp. If you're driving low impedance speakers (e.g. M&K, KEF), or speakers with large variations/dips in inpedance (e.g. B&W, Quad), then a cheaper integrated amp may have difficulty at very high volumes. The weight of the receiver can give you an indication of the capability of the power amp, e.g. my 90 watt Denon is ~10 kg, while a 140 watt THX Ultra Denon I was looking at a few days ago weighed ~20 kg.
The digital processors will be of higher quality in more expensive receivers, the result being better signal-to-noise, dynamic range, and digital filter/DSP quality.
Specifications are often very vague in all but high-end gear. For example, you may get specs on for DIRECT/ PURE DIRECT modes - this doesn't tell you the performance in 5.1/7.1 modes. I get the feeling that the engineers at Denon/Marantz/Sony etc. send their test data to the marketing people first, who then delete all the bad sounding specs.
One thing that may be worth noting is that HK and Marantz have, at least in the past, downrated their power amps compared to other manufacturers, to allow more for headroom. Therefore the best thing to do is to go on power amp test data provided by an independent review.