I’ve been through phases of obsession for both bands and I really don’t think you can compare them like for like. The Beatles will always be viewed through slightly rose-tinted glasses (probably rightly on the whole) as innovators and a symbol of the ’60s, (the latter primarily because they split in 1970!). The role of producer George Martin can’t be underestimated either. Beatles albums were more than just the sound of 4 blokes in a band.
Anyone not convinced of their worth tho’ should read the late Ian MacDonald’s excellent Revolution in the Head. Then it’ll all make sense! 🙂
I think the fact that the Stones still continue to record and tour doesn’t help the debate. Their output probably post-Goats Head Soup (1973) is patchy at best but can you really compare Exile on Main Street to, say, Abbey Road? Almost certainly not.
The simple truth, IMO, is that both were truly great rock and roll bands who really only shared (briefly) a place in time.