Beatles were always my favorite band but I have really appreciate the Stones lately. So, I would vote Beatles but I do think the Stones are second.
Street Fighting Man is too macho. I don't recall Stray Cat Blues, I'll give it a listen. I'd like to add Salt of the Earth, for sure, and Let's Spend the Night Together still makes me giggle (how SHOCKED people were, and it sounds so tame nowadays!). I like their cover of My Girl.
WTF????? Anyway, if you think SFM is "too macho" then I don't think you'll be too fond of Stray Cat Blues
Personally I think Led Zeppelin is the greatest band ever, but at Odds request I wont get into that. I have to say Beatles although I own both bands entire discography. I would get more in depth with my answer but I'm currently serving on a jury at Maricopa County Court House. What ever happened to a "speedy trial"?