The most dramatic changes I've noticed with my setup have been as follows:
1. Using power amps in place of the onboard amps in the Yamahas. The sound seemed to become more effortless, unfortunately this only served to highlight the lousy noise floor of the Yamaha kit I had. Very hissy!
2. Going from the Marantz to the Tag. Huge difference, razor sharp soundfield, excellent effects steering and it does pretty well in stereo as well
. Sounds good with my PS2 as well
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I used to get really hacked off when I had the E492, the amount of hiss it would generate was truly annoying.
In answer to your question, I think I would probably upgrade the amplification first and then the processing side. Of course this all depends on available funds etc. Better amplification will maximise your current processing, changing the processing side gives you the chance to take things up yet another notch.
As to which is compromised on most in a budget receiver, I don't think you can generalise it to any sensible degree. It will vary from unit to unit, but my thoughts are that the first thing to be changed/uprated should be the amplification. I looked upon my Marantz as a stop-gap until I laid my hands on an ex-dem Tag.
You could do something similar, for example an ex-dem AV32R or perhaps even a Cyrus AV5. It all comes down to what your priorities are and how long you want to wait. My "killer" feature was Pro-Logic II, especially with a large VHS collection and a PS2.
Of course the best thing to do is find a dealer who will loan you a machine so you can judge the impact with your setup. Then let your ears do the rest!