I'll try to bang out my take on it.
Snapchat is somewhat unique. I won't touch on its "nudez" reputation, since that's famous enough.
Sure, WhatsApp and Facebook Messenger are better messengers, but since Snapchat is fast, cleans itself up, its "cheap" and the bar for messages is then set really low.
The others don't really let you share "stories" to friends. But why not post to social media you say? As I said, the "bar" for snaps and stories is much lower, so its great for more mundane things, happenings, etc. Things you wouldn't post permanently, but are still nice to share. The comparison is somewhat apples to oranges. Snapchat is more spontaneous and whatnot.
You can easily take a photo, draw on it or caption it, send and move on with life in one fluid motion. Few others do it. CyberDust perhaps, but it doesn't have the mindshare.
I know I'm missing many parts of the puzzle, but I tried.