This article is from the UK, where firearms only account for 2.5% of completed suicides. In both the US and the UK, men are generally more likely to succeed even after accounting for their chosen method, e.g. they take larger overdoses within the same drug class:

https://www.sciencedirect.com/science/article/abs/pii/S01650...

https://jamanetwork.com/journals/jamanetworkopen/fullarticle...