Why? Well, there could be multiple answers, but essentially there's one main reason: it's just dead simple, while vundle and other ruby-inspired ones are not. Pretty much for the same reason I like pathogen+git thousand times more than emacs' package manager.
So even if it could be arguable that pathogen is better than vundle, there's completely no reason not to advise it.
The major feature is that it can install plugins in parallel. I've switched from vundle to it and have been quite happy.
pathogen loads the plugins which is all I need. Does Neobundle do something else?
Pathogen loads plugins, but it doesn't manage them. Neobundle lets me list some plugins in my vimrc and it'll take care of installing them, updating them, and even only loading them on filetypes where they're useful.
Pathogen does none of that and I find every one of those features useful. One of the big ones, honestly, is just the simplicity of listing a new bundle in my vimrc, syncing it to all computers, and having it deal with getting it. Much better than syncing large git repos across computers.