I read that Bradbury book as a boy, of course, and quite a few others of his. I think my favorite was The Illustrated Man. Anyway, you are right about it being cobbled together from a lot of different stories and they were published over a period of a few years. I reread it recently and enjoyed it a whole lot; that story "There Will Come Soft Rains" is still amazing. I guess there are a few clunky ones in there, but I still loved it.
I think the major difference is that those old stories were written for a variety of adult publications, like Maclean's, and more traditional sci-fi pulp magazines. They were not written for children per se, though obviously children and young adults find a lot to like in them. I suppose for many years science fiction was regarded as a genre for children, so that's partly the reason some of Bradbury's books are thought of as young adult. It certainly wasn't a choice on his part to write purely for a younger audience.
Certainly there is more cerebral sci-fi out there, and stuff that's better written, less nostalgic (though I personally love that about his books), but I doubt you'll find a better book to introduce the genre to somebody with.
Here's a Soviet cartoon for "There Will Come Soft Rains":
