I was born in 1950 and so grew up through the whole 60's beatlemania et al. The Stones were basically a chicago blues cover band in the beginning but live they were much different to the other bands around who all had professional managers who groomed them for success in much the same way as the Simon Cowell's of today do. The Beatles had the boy next door thing off pat while the Stones had that bad boy image your parents warned your sisters against. Until Jagger and Richards got their song writing going the Stones were in trouble getting a single until Lennon and McCartney gave them "I Wanna Be Your Man" which was their first chart hit then Mick and Keith figured out their songwriting. But you are right the Stones were hard to market in the early 60's and didn't really become the force we know until the late 60's and became the greatest rock band of all in there prime.What I don't understand about the Beatles/Stones era (which I can only look back on for the most part as I wasn't born until the end of 69) is that to me looking back the Stones didn't really hit their stride until the Beatles were pretty much over. To me the Stones didn't really become a 'great' band until around 68/69 with Let it Bleed and Beggars Banquet.
Before that they seem very 'patchy' especially on the albums. Is it mainly because the single was still king and The Stones managed to pull out a cracking single every 6 months? None of the albums before that are even close to the Beatles albums of the same year imo.
... and personally I think they trailed off quite badly after the 70's too, I'm not into their 80's stuff at all.
All of which is a long way of saying why they don't get in my top 10. I quite curious how people younger than me view them, especially as they are still around as a band. I can't imagine my kids would understand their significance at all.