For me, personally, I would go for the "anything" web host because I know how to install software myself, and I might want to do something else with the space later.
If I were just getting onto the Internet today and didn't know any better, I might not realize that I could install my own scripts on one of the general hosting web sites, and so I might go for one of the "blog" hosting sites. There's always the chance, though, that if I ever wanted to do anything else, I might go with a different hosting company - one specializing in "that" service. (Or maybe not. I don't know.)