That’s an interesting thread with thoughtful posts…
I’m always triggered by such questions because when it comes down to « musicianship » most people always assume U2 are very weak.
Musicianship, skills, talent… are all very subjective notions. So, when we discuss them it says more about us and what we value than it says about the people we discuss, I believe.
That being said, I myself prefer to rate artists and musicians in terms of creativity. How much they do/did their own thing and what they bring/brought to the table in the grand scheme of things.
To me, art is a cascade going from cave men to now. All artists stand under the influence of what was done before them, contribute and have younger folks being influenced by them. Teardrops in the rain.
So… to answer the question, I think both bands managed to build their own sound and bring something valuable, but we all know that, here. The difference is probably that U2 are quite the shapeshifters when REM developed what sounds to my ears as a very repetitive formula.
If I got to compare individually :
Vocals / lyrics : I’ll take Bono over MS any day. A way broader range/contrast. I cannot for the life of me quote an MS line that means a lot to me. I can quote dozens of Bono’s. MS has a real vocal signature, instantly recognizable, though.
Guitars : Edge started by developing his own sound and method, then expanded his palette. He’s unparalleled in that sense. No one ever did that. Not before, not since. Peter Buck has a signature but it’s way thinner. But PB comes down from a line of US guitarists such as Neil Young so he’s more easy to get into and « traditionalist ».
Bass : Adam is way more skilled than most give him credit for. An awful lot of U2 songs have strong bass hooks. That said, MM is a broader musician, not just a bass player. He also has a more subtle approach, sometimes using just one note to make his bass line go from good to exceptional. I’m thinking Losing my Religion, for instance.
Drums : sorry but REM’s drums are, again, on the traditionalist side. To me they don’t bring anything new to the table, even sometimes dragging the band down. A real weakness.
Larry’s sound, again often underestimated, was highlighted by Bram’s recent stunt as U2’s drummer. It sounds like Larry, but isn’t quite like him. Larry has a strong touch that allows flow. Bram hits things but doesn’t have half the flow.
Let’s put it this way : if you place any drummer in REM you have the same band. If you place any other drummer in U2, it’s a different band, in terms of creative process. Bram did ok because the drum patterns were already written. Had he been in the studio to contribute for Achtung Baby, for example, the result would have been, very, very different.
So… my take is that REM gets more recognition because they’re in the line of US bands and songwriters, with just enough character to stand out. U2 made their way from the gutter of « musicianship » which was once their strongest asset. They explored uncharted territory because they were not taught. And it’s interesting to note that the further they got from that approach, and the closer they got to REM’s traditionalist approach, the least interesting they became. And that’s due, in good part, to the fact that artists like REM get more recognition. U2 are jealous of that.
So… it’s not too far fetched to say that, the more we underestimate U2’s original approach and the more we embrace the traditionalist approach, the least interesting U2 get. We contribute to make them less interesting.
Know your strengths.
Damn, you've got me on your overarching point about talent being a rather nebulous concept.. But I too care far more for an artist to be at his greatest creatively than talentedly. I thought this thread could spark some interesting conversation, and uh, well, I can a prize for that.

Going one by one...
What laoghaire said of Bono's heartfelt lyrics makes a tremendous point; I was trying to keep personal "feelings" out of my comparisons, but I can't deny that I am a massive Smiths fan, a massive U2 fan, and a massive Wedding Present fan... all terrific bands which so draw me because their respective lyrics truly showcase great singers singing for the reason I'm drawn to muisc
period.
I appreciate that you mention Peter Buck has
a signature whilst singing of the praises of Edge's development as a guitarist over tune. In terms of talent (sorry, Soloyan), Buck is the better, I believe, but I personally take more away from Edge's evolution as well.
And yeah, Mills a true polymath in the world of music. It's hard to argue who's the greater bassist; for me, it's Mills, for you it could very well be Adam. Thinking on all of the gorgeous soundscapes that he was responsible for on albums like Automatic for the People, the precision of play on Out of Time, or the electricity he puts on Monster, it's not a close contest it's me.
Besides beat-making, I hardly know anything about drumming. And while I haven't heard much of Larry's stand-in for the Sphere shows, listening to U2 as I currently am, you're right about the nuisance that Larry's sui generis style brings to the table. His importance to U2 is eminently than Bill Barry's was to R.E.N.