I believe that, on average, women are better in expressing their emotions - while most men suck at it (often because they aren't aware of theirs). As a counselor, I see it all the time.
I think that skill alone generated the belief that women are better communicators (that, and feminist propaganda insisting that women are always better somehow).
But apart from that, it mostly depends on the individual; and often women are awful communicators because they are emotion-centered and they think their emotions are "the standard" ("I feel this way, so everybody must feel the same"). Because of their being emotion-centered, they hardly can be objective - something most men are better at:
- Man: "Look, these are the facts, deal with it".
- Woman: "But I FEEL differently, so those facts cannot be true".