I think price range really does matter. I was looking in the $800 - $1500 range. I really expected to like the good integrateds better in this price range (no interconnects, synergy, etc.). But the opposite was true. I did head-to-head comparisons, and found separates beat the best integrateds in my price range easily. Also there was much more variety to choose from. I ended up with a nicer pre-amp than amp, still in my budget, with my next upgrade already planned out (a better amp someday).
I'm not sure why the separates sounded better, but I suspect the answer is power and current. I got my Rotel power amp (135WPC and seemingly plenty of current) new, cut-rate at $400 (previous year's model). The integrated's topped out at 60 to 75 WPC. My speakers aren't particularly efficient, and my room is large. The integrated's sounded thin in this setup. Also the separates had much better channel separation ("soundstage").
Another reason this may be true has to do with physical design. I opened the amp at one point. There's just all this room in the box. The parts are nicely spread out, nothing has to bunch out at all. I think it's easier (that is, cheaper) to design a nice-sounding piece of equipment if you have lots of space and not too much to cram into it (not to mention separate power supplies for pre and amp). Of course, if you are short of space to *put* this stuff, that's another matter...
This is not to knock integrateds. The more expensive ones are higher power (100 or even 150WPC). And people swear by the Plinius, Bryston, Classe, and other integrateds. But you start at about $2500 list for these better units. There were none to demo in my area.
Most people will tell you that integrateds are better at this low price point, but that wasn't my experience.
Best of luck in your search!