The Roth-era was much better, less because of Roth than because Eddie Van Halen lost his knack for great guitar hooks and got too fond of keyboards around the time Hagar joined.
Bob Seger or John Cougar Mellencamp?
Mellencamp. Seger is a good songwriter but too earnest. Mellencamp can leaven the social commentary with a bit of wit on occasion.
Marshall Crenshaw or the BoDeans?
Marshall Crenshaw all the way!
(And I, too, favor Mellencamp over Seger.)
Public Enemy or A Tribe Called Quest?
I’m going to take the “Boston vs Kansas” one that looks like it got missed. Tough choice - both were great bands with unique sounds, but I gotta go with Kansas because I really enjoy their longer prog-rock songs, and I always thought Steve Walsh had a hell of a set of pipes.
Wilco or Son Volt?
As much as I really do like Son Volt, I have to go with Wilco on this one.
Okay, well, since no one seems to be biting vis-à-vis PE v. ATCQ, I’ll toss out two WOEFULLY underrated acts from the MTV era: King’s X or Jellyfish?
Jellyfish! I can’t believe I missed them the first time around — so good.
Cheap Trick or Big Star?
Cheap Trick, all the way.
Hank, Jr. Or Hank III?
Hank Sr. 
Sorry, I’ll let someone else answer this one.
Hank III, because his music is truer in spirit to that of his sainted granddaddy, and because he hasn’t become chums with fucking Kid Rock.
Okay, I’m gonna pose this query once more: A Tribe Called Quest or Public Enemy?
ETA: I must say, though, that songs like “The Conversation” and, especially, “Family Tradition”, are damned fine examples of the country music milieu.
Public Enemy
ZZtop or J. Geils Band?
ZZ Top. Though, I might pick J. Geils Band tomorrow.
The Who or Yes?
The Who (by a smidge)
Rush or Blue Öyster Cult?
The Who, naturally.
Massive Attack or Portishead?
This is a close one, but for me, I like the overall sound of Massive Attack better. Trip hop is a little out of my usual wheelhouse, but I’ve downloaded a handful of Massive Attack songs and they are growing on me.
Up next…Grace Potter? Or ZZ Ward?
Although I like BOC, this is no contest. Whether looking at songs, albums, musicianship, or just about any other criteria, it’s Rush all the way.
Try the entire Mezzanine album as a whole. It really is a work that I feel works best start-to-finish, though I do love some individual tracks on it. Really moody, suck-the-light-out-of-the-room music. (I don’t mean that in a depressive sort of way, necessarily. It’s just atmospherically very dark.)
I think Rush had a lot more good recordings, but in their prime, BOC were a much better live band.
Ed Sheeran or Sam Smith?
Sam Smith.
Steve Marriott or Steve Perry?
Steve Perry. Beautiful broadway voice.
Britney Spears or Beyoncé?