Significance sums it up. The Beatles were significant on a cultural, sociological, political and musical level. And took in a comparatively short time a huge leap in development dragging a whole era with them in the process.
Against that, none of the other bands (none of which I find abysmal) qualify:
Led Zep: A pivotal hard rock band with influential riffs, but hardly any cultural impact unless Hammer of the Gods seventies rock star excess is important to you. Or if you're still a Viking, long may you row in the land of the ice and snow. By that time John Lennon has/had already discovered the joy of baking bread for his son. He was way ahead of Led Zep.
Rolling Stones: Perhaps the world's greatest Rhythm'n'Blues band, but the Stones never pushed the envelope of anything. "Blacker" in their music than the Liverpudlians, but also - by design and intent - more limited. It's only rock'n'roll, but we like it.
Velvet Underground: A cult band, very much restricted to urban circles. Ask your Granny to hum you a song from them. She might have been around, but she won't remember a tune. (I'm not sure how the fact that the Velvets had no tunes to speak of plays into that argument though.)
U2: I won't slam U2 or Bono's engagement for rock- or pop-ulterior causes, but by the time U2 arrived on the scene, the Beatles had not set just one mold, but dozens of them. Bono & Co sometimes attempted to break their own mold, but then generally returned to what is expected of them (to be fair: the rock/pop audiences today being also much more segmented and set in their hearing habits than in the sixties). Plus: Living on the right side of the Irish Sea is what it's all about, obviously.
Radiohead: We'll talk again once they have written one happy song in their ouevre, ok? Life isn't always happy, but it's not always miserable either, except in Radiohead songs. The Beatles were emotionally varied in their music, Radiohead just raises a need for varied anti-depressants. All of Radiohead should be force-fed with "Good Day Sunshine!" for a year or so. The trouble with Thom Yorke is that he likes to be submerged under the sea, but forgets the Octopus' Garden fun part of it. Lighten up, Thom!
Tom (not Thom!) Petty & the Heartbreakers: The only thing that is
not conservative about Tom Petty is probably how he votes. His music is an Americana almanac. A very good one, but you tell me when you were last surprised by a Tom Petty song. (Hey, Last Dance with Mary Jane surprised me, it was such a weak chorus melody for his standards!)
Rush: The Beatles not only sang about girls (but not only),
they were also liked by them (but not only). No girl ever liked Rush (transgender Rush fans don't count, they sell their Rush collections once they grow breasts), Ayn Rand excepted of course. Bands that only cater to one half of the world population - Eight Days a Week in weird time signatures you can't even twist and shout to! - don't qualify. BTW: Allan Holdsworth ain't as important to music and youth culture as Jimi Hendrix either. He dresses worse too.
The Band: Great group but again purveyors of Americana. Too rural. If Bob Dylan is Cliff Richard, then they are The Shadows, they even have an Apache (or something close) among them!
The Clash: Do not mistake attitude for influence. Even Green Day owes more to The Beatles than to The Clash.
Bruce Springsteen: For all his merits lyrically, there is hardly any musical progression in the Boss' work. Another Americana merchant. If you rerecorded his first album today with a better sound and released it, no one would notice a difference, and if you shipped his newest album back in time, circa 1972, people would only be surprised at the sound quality. Ronnie Montrose once said: "Musically, Springsteen's sound is as constrained as AC/DC's. As are the expectations of his audience as regards his music." That said, people from New Jersey shouldn't be allowed to be contestants anyway, some decorum please! You can't allow everyone in.
The Replacements: The Re-who?
I've never seen rip-off copies of their releases on Third World markets in Bali and Marakesh.