A lot of this discussion seems to be ignoring the real question in the thread. It's certainly possible that some areas of violent crime are more evenly distributed between the genders, domestic violence being one, but there can be little doubt that violent crime as a whole is dominated by men. How many muggings are by women? How many murders? How much gang violence? How many militias and suicide bombings? Women are certainly represented in all these, but there's really no question that men are involved far more.
There are some obvious reasons for some of this. To start with, culture and tradition is clearly a big influence. For example, I deliberately included only informal militas and not armed forces because until recently women simply didn't have the option of joining, and even now they face significant restrictions. This means that you can't really compare women and men for legal violence, because they haven't been given equal opportunities to be violent. However, this also means that men are often raised to see some violence as a good thing, and are even encouraged with things like play fighting while growing up. Women generally have no such encouragement or pressure.
Without addressing whether men are more inclined to violence, there are some obvious reasons why men have more opportunity to be violent. Plain size and strength are clearly important. If a 7 foot, 20 stone man stops me in an alley and demands my wallet, I'll think rather more than twice before arguing even if he doesn't have a weapon. If a 5 foot, 8 stone woman does the same, I could probably beat her even if she has a (non-gun) weapon. The same applies to most violence, criminal or otherwise. Regardless of their inclinations, women, on average, just aren't as physically capable of being violent. This also addresses the issue of severity - even if a woman is violent she will, on average, be able to cause less severe damage.
Rape has been mentioned, and is again an area that is easier for men for one simple reason - errections. It is generally far easier for a man to rape a woman than for a woman to rape a man. This is also true for cases where claims of rape are questionable due to drunkeness. If a woman is drunk enough to be considered unable to consent, she can still have sex. If a man is that drunk, it's quite likely he couldn't have sex even if he really wanted to. This means that, whether you consider such cases spurious or not, men just don't have the same chance of being on the receiving end. Sure there are various different circumstances involving who does what to who, but in general, men are far more capable of rape than women, even discounting the physical strength issues noted above. On the inclination side, a man does not risk becoming pregnant from raping someone, whereas a woman would, so even with all other things being equal I would expect less rape by women.
Put all this together and it seems clear that women don't have the same social pressure towards violence, have less opportunity to be violent, are less capable of carrying out violence and can't do as much should they choose to be violent. All on average of course. Are there areas where women are as violent as men? Sure, incidence-wise at least if not in severity. Does this mean women are as violent as men? Obviously not. And that's all before you start considering hormones and possible genetic predisposition.