While working a 12 hour night shift in a QC/R&D lab I was asked this question and simply answered, "Roth." Later I realized that the lady was asking as a conversation starter to pass the lonely, but hectic night. I should have explained my answer, but wasn't even sure why I'd pick Diamond Dave. Maybe it was because I'd seen him (minus Van Halen) in concert. Maybe it was because Hagar was pop at the time. Or, maybe I was going with the answer I thought she would give since she was a few years older than me.
Regardless, the first Van Halen album I ever owned was OU812* and that was a copy. I played a little of "Black And Blue" on guitar from that album. I'd also attempted to play "Spanish Fly" from Van Halen II.
My favorite Hagar song is "Right Now" from For Unlawful Carnal Knowledge*, but that was probably more for the video than the vocals. Still, I could argue that Hagar is a better singer, but Roth has more of a rock voice and energy. It's hard for me to pick a favorite Roth song, but I think he was at his best as a singer on his solo Eat 'Em and Smile* album.
*insert stupid album name joke here