I personally think both bands made significant impacts. The Beatles may have made a little bigger impact but The Rolling Stoles made quite a big impact as well.
I'm not a very big fan of either of the two, but I have to agree with the pool that The Beatles are a lot better. I can't really get into The Rolling Stones music.
Really, I think this just matters how who you talk to. I think the Stones hit home more with classic rock fans, but the Beatles bridged past the classic rock genre.
I think a more fair comparison would be Stones vs. Zeppelin.
Not really a big fan of either but I would prefer Rolling Stones if I had to pick between the two. Someone mentioned Led Zepplin so I wonder how people would vote in something more like a Led Zep Vs Black Sabbath or something along those lines instead of that Stones vs Zep idea