A lot of good points I guess, I have also found that a $40.00 7-band EQ pedal can remove mud, add mids, etc. and judicious use of the level control can have a huge effect on the "feel", overdrive, compression, etc. by matching the signal level to the first stage of the preamp. It's a swiss army knife. I have one humbucker guitar, with medium output pu's that will make any amp I have too saturated/compressed and distorted. I bring the level down on the EQ, it cleans right up and becomes more dynamic. If I use the volume on the guitar to do this, I lose some high end. Also for this guitar, I pull the 200 hz slider down a little to tighten the bass up. My Dano U2 has very low output pickups, so when I use that I bring the level slider up just slightly into the boost zone to achieve that tone I'm looking for.
I'm sure different pickups can alter a guitar's tone/feel/frequency response considerably, but I think a lot of that is simply how the relative output level of a different pickup drives the first gain stage in an amp. I played a friend's cheapo import SSX Stinger that I had just fixed and restrung a couple of weeks ago at a little gig after breaking a string on my strat. That thing sounded awesome!! The pickups were a little higher output and were at a perfect level for my Hot Rod Deville's preamp, making it sing, but I gotta believe that it was just at a magic level for that amp, in that room. When I had played that guitar at home thru a different amp, it sounded ok but nothing special.
Anyway, how the hell do you sift thru the manufacturer's marketing department's lingo and know which model pu would be right for you??? Terms like "smooth buttery mids", "warm highs", you know the crap I 'm talking about. I still can't decide if I need the Buttery Mids, Low-end grind, or sweet top end...so I guess I'll keep my money instead of experimenting with $60-$100 coils of wire. (what the hell do buttery mids sound like, exactly??)