A debate that will rage indefinitely.
The fact is, both singers recorded some great songs and albums with Van Halen.
The older I get, the more I prefer Sammy Hagar. Van Halen with Sammy as the vocalist was much more mature and polished. The downside of that was they were more commercial and poppy. Sammy Hagar was always a better singer than DLR, and that's more true in 2018 than ever...I agree with you that Diamond Dave just can't sing live anymore.
When I was younger, especially when I was a teenager, I would have quickly and enthusiastically said that DLR is better. Van Halen's classic era stuff, with DLR, in the late 70's and 80's, was fantastic, although not all of it has stood up to the test of time. They were immature and silly, and those early albums (except for the '78 self-titled debut) were short (just barely qualifying as an LP in most cases) and yet still about 50% filler. Which is true of a lot of rock albums in that era, when acts were expected to crank out a studio album every year under their contract with one of the big record companies.
In 2018, I choose Sammy Hagar as my answer to your question. But I love Van Halen music with DLR, including their hit song "Tattoo" from a few years ago, which was excellent.
https://www.youtube.com/watch?v=3WfQ-hV3WtA