Wow, two of you. I almost blushed.

Nah we're just trying to argue Elvis vs. Beatles for the top spot.
Cultural Impact, I'm pretty sure it's safe to say, is Presley's.

But they virtually tie in each of the other criteria.

Thats exactly what I've been saying.

If they really do tie in the other three areas, then Elvis would win.

I'd say they're tied everywhere. I'd also say that whole discussion is hairsplitting. As long as one of them is at #1 and the other is at #2 I'm absolutely fine with it. I'd also say that seems off-topic here. I'd also say I'm just going to bed now.

Wikipedia's page on "Stairway" says that it was the most requested song on FM radio in the 70s and offers a Zep book as source. I can tell you that when I was working in classic rock radio about ten years ago, it was clearly the most-requested song. I don't know if there are numbers to back that up, but if you look at classic rock radio surveys, it is number one on most.

That's what I was trying to say, thanks.

That's what I was trying to find in Neg's posts, thanks.

Given that, I would say Stairway takes popularity, slightly.

Yup.

Popularity: Stairway slightly
Musical impact: tie
Influence: SLTS by slightly more than Stairway takes popularity
Cultural impact: I'd say SLTS easily. That song really changed the more than just the music landscape. Nirvana and SLTS were the figureheads of alternative culture going mainstream in the early 1990's.

Influence would be tied at best.

What did Stairway influence except power ballads?

What did SLTS influence besides alternative rockers?

Even if the influence of SLTS is limited to alternative, that still beats Stairway whose only discernible influence is on power ballads.

There's no way of proving that, either way, though.