It depends. On a lot of things. Mainly tho, if both are operated within spec, level matched and you remove any kind of sound processing or dsp then yes. Everything being equal it's unlikely you'd be able to pick which was which under blind testing. Now the $4000 Rotel will likely have more power, better parts, better build quality and the ability to drive more difficult speakers with no issues.
So it's not like you're not getting a better amp. There are reasons to spend more money- to a point. I'd argue $4k is an awful lot to spend on any amp, but some folks take pride in ownership and have the money. At the core tho, most of the competent manufacturers have gotten amps literally down to a science and they all have the same goal in the end. Accurate reproduction of a recording. If you think about it, they should all sound more alike than different. If not then someone's not doing it right.
You speak the truth grasshopper.
Put two units within the spec of the weaker unit, eliminate DSP or extra processing, and attach speakers that aren't a problematic load and you'd be super surprised and what you can't detect in a genuine DBT.
We have been conditioned since early childhood to believe that a more expensive item is "better" .
In our hobby however the question of "is the difference audible?" should always ben considered and most times it is discarded in audiophile discussions. Numbers upon numbers get heaped upon us for those high priced items.
Great. That means there's something going on that's good. But is that goodness audible? Not "golden ear" audible, but realistically audible to a real person sitting in a real room playing real music?
There are forums out there who's goal is seemingly to spend as much money as possible to acquire a system and then spend as many paragraphs of purple prose as possible to describe it. The AH is sort of the antidote to that line of thought. Prove it seems to fit the AH. Make a claim? Well, prove it with something solid like measurements.