My friend and I kinda of resemble that dynamic. He loves some of the shittiest songs (imo) because of interesting lyrical content, where as I totally ignore them. If I like them it's because of how they were sung not because of me diving through looking for "meaning".
That's why after all these years Pinback is still one of my favorite bands. Their voices are just another instrument in a lot of their songs, since it sounds like Rob Crow kind of mumbles through them all, and they're usually sitting a layer or two down in the mix.
For example: http://www.youtube.com/watch?v=59cQWw9ctOA (not the greatest quality I know). It's the way he sings / shouts "Stop! It's too late! I'm feeling FRUS-trated!" that draws me in.