Would you rather listen to a flat or falsetto voice?

Basically, I'm a terrible singer. I wouldn't go as far as to say tone deaf, but just a kind of voice that people wouldn't really want to hear. Anyways, I personally believe, and have been told, that I have a better falsetto voice (i.e. I sing better at a higher pitch). However, I also think that a falsetto voice can be way more annoying than a flat voice (which is how I usually sing normally).

So, my question is, would you rather here a normal range song (by normal, I mean something that wouldn't require the high pitch range of a falsetto voice) in a flat voice that doesn't really sound that good, or in a better sounding falsetto voice that doesn't really fit with the song?

I'm speaking in general terms here, but if you want to put it into context, I want to make a public performance in which I sing Chasing Cars by Snow Patrol and am wondering in which voice to sing.