I would say men are better at succeeding because men in general are results driven. "Set a course and get on with it". The methods aren't the reason but a symptom, men will pick more effective methods to achieve the result. Personally I'm not going to try to od on pills or cut and see if I bleed out. It'll be one that is a high percentage method. There are reasons more men may ctb now but if the success rate has stayed the same over time, even when total deaths is low, I would put it up to what I posted.
There are less support systems for men but that's more of a breakdown in society to an isolated online world. Men who came back from horrendous war experiences continued to live even though they've seen the worst. They had organizations and activities where they could be comfortable and deal with their issues in their way. These were social groups. Now those groups have died out and more young men are online only, not interacting in person, which I believe effects how you interact and respond. Saying "man life is really sucking" to an online friend or even on the phone is different than saying that to someone's face and seeing their response. I notice this personally, and I have a low online presence because of this. I'd rather hang out with people than be online, and I'm normally an anxious quiet person. Having a group that welcomes you when you show up and do a shared activity, for me, is a big uplift; this goes for men & women I believe. I'm in a model building group 1/month and play games with others when I can. We get some new people, usually guys, see the model group (it's a a hobby store) and we always chat them up. I think many of them see a group of guys building models, bs'ing, laughing at jokes, talking shop, and griping about life and they form a connection. We get new people joining up. When you don't have a group of people or a person who's not intimately involved with you (relative, partner, etc) you're alone dealing with issues and I don't feel online fills the bill fully. Like only eating chips for food; ya it's technically food but not good food.