I don't have a definitive answer to this, but based on the first 2 episodes of Gatchaman Crowds (all that has aired so far), at the very least there's no clear connection between the two series. If they are in the same universe, the characters in the two series don't seem to be interacting at all. There are definitely references to the original series, e.g. all of the members of the Gatchaman team in the original series have counterparts in Gatchaman Crowds, and many of the concepts stayed the same.
There's good reason to believe that the two series are in different universes. In the original Gatchaman, all of their powers were, at least in principle, just the product of science and technology. In Gatchaman Crowds, by contrast, their powers are of some sort of mystic origin. It's not yet clear how they work, but they aren't purely within the realm of science fiction anymore. This rendition of Gatchaman is thus fundamentally different from the original, and probably only makes sense in its own universe.
The Wikipedia entry for Gatchaman Crowds seems to agree with this, describing Gatchaman Crowds as “based in the Gatchaman universe,” which would seem to preclude it from being in the same universe. However, there's no solid source for that statement, so it's at best questionable.
Of course, this answer could still change (at least until Gatchaman Crowds ends) but for the moment it seems more likely that they are in different universes.