Wow, I was a HUGE fan of all three when I was a young whippersnapper.
Ok, let me try to reason my way through this...
Dokken's catalog hasn't aged particularly well (and I never got into Lynch Mob either). There are a few songs that I still enjoy from time to time, but overall, it doesn't really do it for me anymore.
Randy's soloing, while brilliant for the time, strikes me as somehow unrefined nowadays. If he had lived, I'm sure he would have continued to grow as a player, but the guys who came after took the things he was doing and went far beyond (IMHO).
OTOH, I love everything about EVH--the playing and the songs. You could put on any tune, from I to, probably, OU812, and I would love it just as much now as the first time I heard it. That goes for the songs, as well as the solos.
All that said, I'm still a fan of all three. And all three did things that completely blew me away at the time. And I still stumble on stuff from all three that I just have to try and learn. Ed just has the edge for me.
All great players! As far as impact on guitar playing Ed by a long shot. Like Hendrix he will always be remembered as one of the guitar players to have a huge impact on what can be done with the instrument.
Edward has made me go WTF several timesIn a fight? Randy loses.
They're obviously all great players, I think I listen to EVH and Randy way more than George Lynch though..because of the bands/songs mostly. I like Dokken (really didn't enjoy Lynch Mob) but they're not Van Halen or Blizzard of Ozz when it comes to consistently excellent songs.
In terms of their impact on the guitar or guitar culture in general, EVH was the "next big thing" after Hendrix. Randy's importance was certainly great, and may have been greater (who knows what he might have done?), but was also magnified by his dying after such a relatively short career. Sometimes I am more in the mood for Randy's classical melodic style (and totally understand people might always prefer that style) but overall, EVH does it for me. Every new album from I to 1984 contained some guitar that made me go "WTF??!!"
George Lynch doesn't really figure at that level for me, great as he is.
From a playing standpoint, Rhoads was phenomenal, but may have had the worst tone ever.