The gunslinger moustache is a casual style and the petit handlebar moustache is a much more perfect style that requires a good amount of product and finesse. It is the style that will force you to wake up 10 mins early and comb, wash, style and apply product to ensure it is perfect all day long.
Also the gunslinger is thicker and bigger than the petite handlebar. It is on par with the handlebar mustache and so there are the obvious differences that you must consider. The gunslinger requires stronger mustache growth and is also not at all acceptable in a work environment.
The petit handlebar is acceptable in work environment, is a sexy style, is achievable even with scanty moustache growth and also is a popular option amongst men. Handlebar moustache style is compatible with almost any beard as well and while it does require good amount of efforts to maintain the style, it is worth the final look!