Yes, I love R.E.M. and have for many a year. Those of you who came of age in the Pop era may not be aware of how big R.E.M. was in 1991 to 1995, when they basically ruled the world. Their first top ten hit was "The One I Love" from 1987's Document (their 5th album -- it also took U2 5 albums to have a top-ten US hit), and then their contract with the independent IRS records ran out and they signed with Warner Brothers. Some hardcore fans have never forgiven them for that (which is ridiculous). Still, there was something very special about a band as commercially accessible and with as much integrity as R.E.M. being on a tiny label, and cranking out quality albums every year back in 80s America. That IRS period is still revered, and there are good compilations available that focus on that period exclusively.
In 1988, Green came out and was followed by a major world tour, at which point the band started getting really big, and not only in the USA. Green rocked a bit, but was starting to sound more 'folksy' and pop-friendly, and when they decided (for the first time) not to tour after their next album, and to play some new, folk-inspired instruments while keeping things largely acoustic, they expected to have a fall-off in popularity. Instead, Out of Time (1991) ate the world after "Losing My Religion", a tune with an obscure lyric and a mandolin as lead instrument, climbed up the world's charts.
At this point, a funny thing happened. The US college-scene, which R.E.M. had always been part of, morphed (and commercialized) into the Alternative Rock aesthetic, which continued to embrace them. Partly as a result of this, Out of Time went to #1 on the album charts while the band were sitting at home, relaxing. They then produced their softest, most melancholy work yet, Automatic For The People (1992), at the height of Grunge, and it sailed to #1. (It did the same in the UK, where it was one of the albums of the decade; they have also been extremely popular in Germany and across Europe). Again, the band didn't tour it, and again it exceeded all sales expectations.
In retrospect, Bill Berry was probably was probably unhappy with these musical trends (the word was he told the guys, "If the next album doesn't rock, I'm outta here!"). Needing to tour again, the group got very self-conscious and made Monster (1994), which was another huge chart-topping hit, but seemed a bit strained and self-consciously trying to be loud and cool. The tour was on a big scale, and had some unexpected setbacks.
At that point, they were easily the 1st, 2nd, or 3rd biggest group in the world, and they got a new contract with Warners, for incredibly huge sums. Since then, they've been less prolific, more "corporate" in career trends and decisions, less complete since Bill Berry quit, and generally less successful -- especially in their home country. Bill Berry, by the way, was not just a drummer, but also a great composer and arranger -- he was the main composer of songs like "Everybody Hurts", one of their biggest hits. And yeah, he probably helped them rock a bit more.
Compared to U2, R.E.M. seemed not to crave or work for massive success so much. When The Joshua Tree brought U2 into the homes of middle-class housewives and Jr. High school kids, the guys seemed ready for it and so firmly grounded that they could handle the incredible success -- it was like they were born to be icons. R.E.M., on the other hand, often made conscious decisions in the 80s to not get bigger (not lip synching in videos, dressing strangely, et al). After they signed with Warners, I think they thought that they'd go a bit more commercial with Green and its tour, and then kind of relax and slow down. I think they had no idea that the whole thing would get bigger and bigger after they stopped touring, and that they would suddenly rival U2 in popularity. When all that happened, I think it put some strains on the group that it never completely resoved. At one point, Peter Buck's marriage collapsed and he spent months, alone, wandering around Mexican small towns. Bill Berry became a nervous wreck and couldn't handle gigging anymore, and quit. His style of working (esp. in the studio) had been more in sync with Buck, who then became a bit isolated and felt ganged up on by Mills and Stipe. The group almost broke up over these issues in 1999.
Basically, the R.E.M. guys are modest, Southern gentlemen, and the U2 guys are high-energy global diplomats, always ready for a night on the town.