Men may be from Mars, but is it a different planet?

The difference in conversational styles continues to stun me.

I recently attended a reception for a group of highly educated and very successful people.  Successful women, including the honoree of the party, who the rest of the attendees were trying to woo, said things like:
- Oh, you probably know more than I do about this
- I can give a lecture, but it's hard to talk about me
- I am not a specialist in this

While men, even noticeably less successful men, said:
- Oh, but you don't understand
- You are wrong, this is not how it works
and overall did significantly more bragging, even for less momentous achievements.

Is the difference caused by nature or nurture?  If it is nurture, then who is doing the nurturing, and, more importantly, why?

More practical question: which way is better?
And what is "better" in this context - leads to greater success, allows for more peace of mind, something else?