If I had to choose I'd probably go with the Beatles, I think they had more memorable songs that can stand the test of time than the Stones (who have had their share as well, of course).
A story in this vein. In the mid 60s, the Stones first hit with airplay in NYC was Tell Me You're Coming Back to Me. One afternoon while I was listening to Dan Ingram, the late afternoon WABC DJ (who also had a jazz show on FM, as I recall), he made a comment on air after playing the Stones record to the effect that he felt the Stones were a poor imitation of the Beatles and he didn't like them. Well, after another record and a few commercials, he came back on and said that the switchboard had lit up due to this comment, so he announced that he would run a contest, $10 to the best letter sent to him telling him why he should like the Stones and $10 to the best letter telling him why he shouldn't. A few days later he announced that a couple of girls had written him a multi-page letter going on and on as to why he should love the Stones, so they won $10; the winning letter as to why he shouldn't like the Stones was simple--they were costing him $20.