First off, let's talk about the difference between sympathy and empathy.
-If you want someone to tell you they feel sorry for you, this is sympathy.
-If you want someone to tell you they've also experienced what you've experienced, you're not the only one, this is empathy.
They aren't the same thing and it's a good idea to remember that when discerning what a person wants out of a conversation.
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I believe this is a generalization, a big generalization. I think this is more a factor based on a person's personality rather than their gender, I'm female, I'm very solution driven, I do value conversation, but if I'm talking to you, it's usually not because I want someone to feel bad for me. If I'm talking to you about a project, I want your opinion, or help brainstorming. If I'm talking to you about something I don't know much about, I'm hoping for your point of view, so I can better understand an issue. I can't small talk to save my life and very rarely find it easy to vent about my feelings (unless I'm pissed off and that's a very different kind of venting than what's implied here, misery loves company).
On the flip side, I have a male friend who's had a traumatic past and suffers anxiety issues because of it, I encourage him to talk about his feelings, because it's not good for him to keep them locked up. When he does, I sit and listen until he's finished and I try my best to offer solutions, if it's a more tangible issue. Unfortunately sometimes there's absolutely no solution that will solve his problems. You can't exactly tell someone who's having nightmares to get over them, in this case, sympathy (or better empathy if you've also experienced it), is the one and only solution.
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Now I'll counter your generalization with a different generalization. I see a lot of custom t-shirts where I work and this saying has popped up a few times.
(disclaimer: This is a generalization, I don't personally believe this myself, I'm posting this to show the outlook goes both ways)
"They're called "man-hours" because a women would finish that shit in 20 minutes"
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All this being said, I did say this is a personality factor, NOT a gender factor, however certain genders may be more inclined to have certain personality types. [http://www.mypersonality.info/personality-types/population-gender/] All that is based on Myers Briggs, so whether you buy into that or not, your mileage may very.