Actually, since men tend to sweat more, men's deodorants tend to be stronger/have stronger scents. I can't use women's deodorant because it just wears off, but when I use my right guard (intended for men) I can go more than two days without topping up (to note, it's a 96 hour one, and i really don't sweat much despite binding). My uncle uses women's deodorant because it's more gentle and he doesn't sweat much, and he finds it works better.
Although, I found in the US the deodorant was basically the same unlike the EU (the difference here is smellable) just with different scents. Over here there's only a few choices in scent that are barely distinguishable, but the selection in the US is huge... I always cave in and buy ridiculously scented products because I can.

Noto Bene: Ditch Axe. Doesn't really work for... anyone, really... and it's more like a body spray. Right guard, old spice, even the adidas brand are all better, last longer, and don't smell as strong. Also, I've seen women mistake Axe for perfume, so it likely doesn't help passing either.