I've been a fan of They Might Be Giants for most of my life and have always been surprised that people universally disagree with me on this.
Linnell's songs tend to be quirkier but also shallower. (State Songs is a good example here - there isnt a song for every state and theyre often abstract to the point of meaninglessness. I expected such a project to have more inspiration behind it.
I've always found Flansburgh's more melodic and thoughtful, slightly better composed, and with a superior singing voice.
Of course they're a great duo and they play off each other's strengths. I don't dislike Linnell at all, just the songs that he sings tend to not be my favorites.