Both Capa and Alekhine would probably face pressure in the opening, since today all modern elite players are so booked up. That said, Capa's choice of harmless yet solid openings, such as the Four Knights, could paradoxically be an asset when playing the modern elite. Once out of the opening, they'd be as dangerous as today's Anand or Kramnik.
If Alekhine and Capablanca were playing today..

Well if they were immortal and kept practicing for a century, even without modern conveniences, then yeah, they'd probably be pretty darn good.
Why is everyone leaving out Carlsen? I mean, he is like top#1 and if not, top#3 always. Yet noone mentions him as someone good. Why is that?


Teleport them here and give them 6 months to a year to catch up on the last century's worth of advancement, and I'd pay money to see either of them at Corus A or Dortmund, etc.

I don't know, it's possible of course. But i doubt one can totally compensate having studied 2 hours a day instead of 10 for a life in 6 months. It's not lack of respect for the great players of the past, but common sense. Supposing Alekhine and kasparov equally talented, these "ambiental" factors must count for something.

Those other factors will count for something, but I don't think they'd be as important as you think. Think about how much time is spent just becoming good enough to never drop a piece, or a pawn, or how long it takes to get to the Expert stage. How much is spent learning the basics of your openings, how much spent learning the endgame? How much is spent getting from Expert to GM? All this time, the old masters have already spent. I say that is the bulk of the study time that those ambient factors account for. Perhaps it's true that Kramnik has spent quite a bit more time since becoming a 2700, but how much more time has Nakamura spent since reaching that level? (He topped 2700 in April 2009) He's not nearly as old, but still plays at or near the same level. Perhaps Capablanca is already 2700+ strength, and also wouldn't need much more time to climb near 2800. Maybe 6 months is too short, but I don't think it'd take very long for them to catch up. Not to mention the excitement that Naka would feel from "wow, I'm playing CAPABLANCA", but that's outside the scope of this thread =)
If Alekhine and Capablanca were playing today the same way they did back then using the same preparation methods and such, do you think they would be as good as they were back then?
There are computers today that can keep modern players sharp. Do you think it would make a difference?