I agree with the aforementioned notion that their importance relies on the general acceptance of their genre by the general public.
As long as the music reviewers and so-called non-artificial music
connoisseurs will prefer
punk to metal, will praise
the sound of muzak, and will dislike prog in general for "taking the music away from the masses" and being "pretentious" (they have done so since the 70's) and general public will listen to David Guetta, Avicii, Pitbull, Skrillex or Flo Rida (or Nirvana, or, if they want to be metal, metalcore), in short, as long as people will be that
shallow and want their music "simple, stupid", I think Dream Theater (or metal in general) will resonate very little.
That's what the music industry wants, mind you, just
kneel and disconnect, accept stupid, because it's much easier to produce stupid.
By the way, even Metallica became famous in the non-metal-listening crowds because of Nothing Else Matters - which is a song important for
what it is (a popular song by a previously thrash band) than any hidden qualities within the song (since it's more or less a mediocre ballad and it's not metal at all).
Dream Theater might be important as far as prog metal is concerned, but prog metal is a marginal sub-genre of a marginal genre itself (i. e. metal) and until more people will consider it important, the legacy of DT is practically non-existent.
No part of me believes they are actually more "important" than Iron Maiden from this point of view, since Maiden's crossover appeal is much greater (definitely more people know them or casually listen to them).
As for Rush, I honestly don't know. I know they're very popular, but that's 1.) mostly because of their synth-rock era (more people like, let alone know Moving Pictures than A Farewell to Kings) and 2.) I believe they're more well known in America (the continent) than here in Europe - here when people talk about prog, they're sure to first name Jethro Tull or Yes, with Rush almost an afterthought. Or maybe it's just the Czech Republic.
This all make me a bit sad, since when I think about the future, say, 60 years from now, there will be
even less DT fans overall, since we're in the minority even now, many of us will be already dead by then and DT will not be only a band playing marginal genre, they will be then already defunct band, a band from history, playing marginal genre. I mean, how many Gentle Giant fans are out there, really?
So I say - f*ck importance, let's enjoy what's good and let's teach our children what good music is. I know it worked for me.