Yes, they do intersect in some areas as you can build CRUD UIs with both. Avo takes it further to give it a nicely designed UI, all the "missing" features like extending the interface, adding custom content, supporting all associations thoroughly and more.

I think of it like the next iteration of these kinds of tools.

Have you built something using administrate?

Yeah, I've used Administrate a bunch. All those things are possible in Administrate as it generates controllers that can be customized, so anything it doesn't do out of the box can be added easily. It's also easy to define custom input types and content types.