Sorry, but to say that Zeppelin never evolved is just patently false and that isn't a matter of opinion. I laid out several musical reasons to demonstrate this and I could come up with more. Oh, and they are also not overrated, that is my opinion, and they are definitely not a "jam" band.We definitely disagree hard on this one, Grant. That's ok. Listen to Between the Buttons then Let It Bleed then Exile then Some Girls then Tattoo You. There's quite an evolution from 60s mod-pop to politically-infused rock lyrics to southern blues jams to disco-punk to stadium rock.
I get that Zeppelin was super protective of who could license their music for moves and media, but The Stones are far more ingrained in the American pop consciousness than Zeppelin. Call it what you will, but that matters in these debates.
The Stones are the better, more impactful band for me. And it's not all that close.
As I said, the Stones did evolve quite a bit up until about Beggar's Banquet. After that, they really just stuck to mostly the same formula. And since you brought it up, Tattoo You is a compilation of outtakes from the previous decade. The fact that that album sounds cohesive is another indication that they really didn't change all that much over the decade.
In terms of "better more impactful band", I didn't offer anything on that. That is opinion based and I think can be fairly argued both ways.