U2, The Police and The Rolling Stones. Although with The Rolling Stones I do quite like a few of their songs, but people always ask "Stones or Beatles?" as if they're just as good as The Beatles. They're good, but I don't find them as good as some other people do.
On the other hand, I think the Beatles often get too much credit and I sometimes see them called the most influential band of the '60s. They were great, no question, but there was so much more going on back then. As for comparisons with the Stones, a lot of that was due to the Stones' brilliant marketing at the time. By positioning themselves as the anti-Beatles, people suddenly saw them as equals, even though the Stones were a lot newer band and didn't yet have the songwriting chops they would later develop. I really don't think much of Beatles vs. Stones comparisons because the Beatles were so much more popular-music inspired and experimental, while the Stones stuck a lot closer to their blues, R&B and country influences. Which is why I like the Stones more, personally. Also the Stones stayed together longer and went through more interesting times, musically. It would have been really interesting to see what the Beatles made of reggae, disco, punk etc.
--Justin