Not to pile on or beat a dead horse here. Clearly I am a guy that believes in "to each his own." I flyfishing for carp, so I am not a purist but I do have a wide range of fishing experience from which to draw. Based on my own personal experience carp are easily one of the toughest freshwater fish to catch on an artificial. I think talking about any fishes "intelligence" is fatly subjective, but carp have actually been studied and shown to learn. One British study revealed that carp individual carp hooked on a food source would avoid that same food source for up to two months. That seems crazy, but my own experience in small ponds with low populations of fish bear that out. I have to repeatedly create new patterns to fool the captive fish in one particular pond. This varies from my (and many others) stories of having a trout break off a fly only to catch that fish later in the day and get your fly back. One smarter than the other? Who knows. There is some science out there on it but I only have anecdotal evidence at best.
The real question is which is more fun, right? And that is totally subjective. It really comes down to method more than fish, right? We all spend more time "fishing" than we do "catching" so most likely we "fish in the manner that gives us the most enjoyment. In my case that would be with a flyrod, stalking large, wary fish in shallow water. For another it might be with drift gear feeling for the subtle difference between a rock and a soft take of a coho, and so on and so forth. There is no right or wrong, just varying degrees of enjoyment with each method.
I would make the statement that the method and the gear (don't use a tuna rod for bluegill, etc) is likely more important than the actual quarry. Variables such as fighting power (carp lead in my book) setting (the sandy? Wow) and table fair (carp lose clearly here,) come in to play but it still really comes down to how you get the most enjoyment from your "fishing" time, unless you spend all your time "catching.". I know I sure don't spend enough time "catching."