As VH is my all time favorite band, I consider myself something of an expert.
So let me explain it this way:
David Lee Roth was a better singer and front man.
Sammy Hagar made Van Halen a better band.
Make sense? Overall, DLR has a slightly better voice - Diamond Dave was something else with those vocals. Plus, as a front man, he brought an energetic presence to VH that only Queen and Kiss had ever experienced to that point, and only Poison and Motley Crue would thereafter.
But with the Red Rocket in Sammy, Mr. Cabo himself, Van Halen became a fuller and far more well-constructed band. The song-writing improved with Sammy working with Eddie, the bass of Michael Anthony was featured more prominantly and technically, and the music itself came together and was mixed better.
Plus, with Sammy, the music got deeper. It was still fun - songs like "Finish What Ya Started" were great. But with DLR, they were a fairly one-dimensional party band. Not many levels.
Sammy also helped introduce Van Halen to the theme album. Look at "ForUnlawful Carnal Knowledge." Of course the ackronym is F.U.C.K. That also happened to be some of their most passionate and sexually charged music.
Eddie, I felt became even more innovative with Sammy. Playing the drill on his guitar in the opening of Poundcake. I mean, holy hell.
And the Balance, the most under rated album of 1995. Check out this excerpt of "Right Now" from that tour.
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This is one of rock's greatest bands ever, and overall, while I loved Diamond Dave's sound, vocals, and presence, Sammy was a superior lead in most other ways.