Selecting who receives is easier, too, because you can uncheck some people. Instagram doesn't have that option, I'd need to create a new list with Facebook, and group texting is a lot more work.
When you share to a feed you'e sending it out for everyone to see. You want to know that people saw it and with services like Instagram and Facebook this is done via commenting and Liking/Favoriting.
With Snapchat you fire and forget. No one needs to like the picture in order for you to feel any sort of satisfaction. The only indicator you get is that it was viewed at all - and with the sort of content that gets sent over Snapchat, that's really all the information you need anyways.
TL;DR: I think the "choose indiciduals to send to" model is more important than the "they get erased" aspect. Of course, the vanishing part of it is what got Snapchat to become popular in the first place so it would be wrong to say they would have seen the same amount of success without that feature. However, at this point, I don't think that is what makes users keep using the service.