I think manly and feminine methods come from different circumstances the genders find themselves in, rather than preference. Women are more likely to seek help for depression, thus getting access to prescription drugs while most police officers and soldiers are men (access to weapons). Men are also more present in shooting clubs, so they also have access to an effective method. Im also only guessing, but I think its safe to assume that the preferred method for doctors for example is anastethics, regardless of gender, since they have easy access and the required knowledge.
"Neutral" methods such as hanging are similarily popular with both genders since their circumstances deny them other methods.