Once in a Lifetime and Burning Down the House are two of the worst songs I've ever heard and I refuse to listen further on that basis.
Those are his worst ones, so you're okay to feel that way.
As for my opinion, Byrne is a better lyricist while Bowie is the better musician.
What? Those are both really good songs. And, between the Talking Heads and his solo work, I think David Byrne has 8 or 9 great albums. The Talking Heads are super accessible and fun, but they have that extra layer of amazing lyrics.
I just find David Bowie's music too eclectic and over-produced. Maybe I'm not enough of a music snob to get Bowie.