Heh - gee, I could guess you're a fellow midwesterner just from the "delicate" way you bring the subject up, LoL...
I'm not a "carp fisherman", but I've caught them with hook-and-line and many springs ago I bowfished for them a couple of years. Oh - I've eaten them as well.
In my part of the midwest they are sneered at by, erm, un-informed people because they are associated anecdotally with a certain ethnic group - in other words, some folks make racist comments about carp (think that over a moment - how absurd is that! It's a fish, fer cripes sake!)
It's a white-meat fish (minnow, actually, I think) so it is about as bland as any other white meat fish. The quality of the meat depends on the polution (or lack of) in the water it lives in, just exactly like any other fish.
Commercial fisherman around here smoke most of their carp catch. Smoked carp, like most any smoked fish, is a tasty snack to me; YMMV. I have also eaten fried carp - tastes like... fried fish. Poaching, broiling, and baking carp are unknown to me, and I defer to M_A_X on those methods - which are probably a better indication of what carp meat tastes like than smoked or fried.
The source of the sneering in the USA comes from who introduced carp when and why: US Grant administration after the Civil War as a food fish. You may fill in the blanks from there - we both live in the midwest, so I expect your local myths about carp are the same as ours. Carp are an important food fish in Asia where they originated and if you look in the kitchen of many "Chinese" restaraunts, you will find one or another variety of carp being prepared (at least, in all the kitchens I have been in locally...)
Hooking one produces varied results, but they are never easy to just wind in unless you are using very heavy line. Sometimes they pull like a bulldozer and sometimes they fight the line like a beserk "game" fish. But the ones I caught have always been interesting on the hook. Bowfishing is altogether different to me and I think carp are the only fish I've ever taken with a bow. Maybe some buffalo or freshwater drum also - been a long time ago.
When I was a kid, one of my neighbors (the term "hillbilly" comes to mind rather sharply) used to keep caught carp alive in clean water for a week, feeding them cornmeal doughballs. I can't say what that did for the taste because that family never shared any <grin>.
If I caught a carp these days I would take it to a commercial smokehouse - and that's my prejudice, because most any other local food fish I simply cook and eat - poached or fried, according to species and my fancy at the time.
I suggest you find someone who smokes fish, try some smoked fish of a species you consider palatable, and then try some smoked carp. If you like it <shrug> go fishing...
<Edit> check this out - start at the bottom with the info and then check out the recipes above. Sounds interesting, now that you "made" me go check this out:
http://www.idfishnhunt.com/eatcarp.htm <end edit>
HTH,
Tom