So here's what we're looking at:

1. Johnny B. Goode
2. Like A Rolling Stone
3. What'd I Say
4. Satisfaction
5. Respect
6. Rock Around The Clock
7. Stairway To Heaven
8. Jailhouse Rock
9. Smells Like Teen Spirit
10. Hey Jude
11. I Heard It Through The Grapevine
12. Good Vibrations
13. I Want To Hold Your Hand
14. Billie Jean
15. The Message
16. Papa's Got A Brand New Bag
17. Bohemian Rhapsody
18. A Day In The Life (Yeah, switched on the whole "3 Fab songs are overkill" thing)
19. Hound Dog
20. Superstition/Dock Of The Bay

???

I'd say that "Stairway"'s leads in popularity and cultural impact far outweigh SLTS's leads in the other two criteria. Stairway is a cultural milestone.

OK, my breakdown with explanations:

Popularity: Hard to measure as Stairway never was released as a single. Stairway is a highly popular tune, no question. SLTS was a #2 US single, and it's at least a well known as Stairway I think (maybe even more).

Musical impact: That one's very close I'd say. Both songs are highly acclaimed.

Influence: SLTS marked the point where alternative rock broke into the mainstream. It helped popularize a genre that has been huge for the last twenty years. Stairway was influential on power ballads which were a huge part of the rock music of the 1980's/early 1990's. Other than that I probably don't understand the nature of Stairway's influence.

Cultural impact: I still think it's hard to tell what is included under this criterion and what isn't. As already mentioned SLTS marked alternative rock's breakthrough, and with it probably other aspects of alternative culture (without me being able to specify them). I don't see any cultural impact for Stairway.

I'm a raging Cobain-fanatic, but SLTS is too high. #9 of all time? Not seeing it.

And how can Papa's be so low? It was basically the song that established funk as a legitimate genre.

I guess an official new editor would be a good thing to really get things going.