When I think of the LA metal of the 1980s, the bands that immediately come to mind for me would be:
Motley Crue
Ratt
Dokken
W.A.S.P.
Lita Ford
Keel
Quiet Riot
Great White
Y&T
Stryper
Black 'n' Blue
Later in the 80's:
Guns N' Roses
Poison
Rough Cutt
LA Guns
Faster Pussycat
Warrant
Mr Big
Bang Tango
Pretty Boy Floyd
I'm sure there are others that I'm completely forgetting. I'm looking specifically at the local LA rock scene in the 1980s. There are plenty of other bands from other locations around the country (and world) that would fall into that "genre" of music, but I'm staying away from those.
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I don't know if I could say which one is "the best" as that is such a subjective term. In terms of success, I don't think anyone could argue that Motley Crue was the most successful of them all, especially of the early 80's, Sunset Strip scene. A lof of these bands were perennial opening acts, or were headliners on smaller venue tours, even in their hey days. Of the early list, Ratt was the only other that continually were a headline act at least in the mid-80's through the early 90's.
Guns n' Roses had the potential to be the single biggest hard rock LA band of all time, but they imploded in the early 90's. Even with that implosion, they still made one of the biggest impacts. Poison was a headliner for a few short years. Warrant had the potential to ride on Poison's coattails, but with the fall of glam metal in the early 90's, they only got 2 really successful albums, and then kind of disappeared along with many others on the list.
So, I probably haven't answered the question, and at this point, I'm not sure that I can.
My favorite: Dokken. In my opinion, probably the most talented musicians in the entire bunch, and vastly underrated and under appreciated.
Most successful: Motley Crue