Even that can be hard to recognize. The Monkees are an obvious example, but so many other bands could fit either bill.
I tend to agree with Dom. Music is so taste driven and the reasons people like/dislike bands are strange/varied/inconsistent. For example, I am not a big fan of the Doors. All I hear are drugs and Jim Morrison seems like the kind of guy whose sole reason to exist was to steal and bed your girlfriend. Those are totally irrational and subjective things. I like rock organs (like Elvis Costello), I like bands who used alot of drugs (almost all of them), and I like insufferable guys like Jim Morrison (too many to name, but everything I've ever heard about John Lennon seems to fit this category) and yet I don't like the Doors. Is that rational? No. Is my feeling real? Yes.
I have a friend who soured on Arcade Fire after going to a concert and being surrounded by obnoxious frat guys. As if that was the fault of the band. How dare they make music that appeals to more than just his demographic.
I do have some very broad, general things I tend to lean towards. I am a sound guy more than a lyrics guy (but I love Randy Newman), I like innovative bands (but love stripped down rock like the Black Keys), I love upbeat music (but prefer Beck's Sea Changes/Mutations/Morning Phase to his more exuberant stuff), I like subtly (but love most rap). None of this makes any sense, but I know what I like and know what I don't like. Oh, and I'm right...