I thought the general trend was:

Men: Fewer but more lethal.

Women: More but minor bumps.

Ironically this is possibly the same trend as suicides,

Men: Fewer attempts because those attempts work first time.

Women: More attempts because a) most attempts aren't fatal, therefore subsequent attempts might be made so mulitple attempts per person, b) 'self harming' is counted as attempts even when it isn't an actual attempt.