The Only Bands IMO I'd every debate about being an equal, better or even in the same league with the Rolling Stones in terns of a cultural, social, or musical prevalence would be:
The Beatles
The Who
Led Zepplin
The Byrds
The Band
Pink Floyd
The Beach Boys
and a few others
but never would I entertain the thought of a comparison between
The Eagles and the Stones in terns of a cultural, social, or musical prevalence.

IMO
The Stones IMO the greatest ROCK N Roll band of all times are only second to one in the overall Spectrum of those 3 catergories, cultural, social, or musical prevalence.
And by being second has always made them a little angrier and a little more edgier the 4 mop tops. That's what I have always loved about them.
IMO
I will also say that when I played live music for a paying public (during the Hotel California days), the Stones covers always got the audiences motors running. There was always a change in the feel and atmosphere of the room when we lit in to Brown Sugar or Honky Tonk Woman.
We played all the above bands mentioned, and the Eagles.

Now let the beatings begin.
I love this place.