Cover, or Original?

Personal experience and preference. I've yet to encounter a cover I didn't like. If I didn't like it, it's probably because I didn't like the original anyway.

I directed that comment to the second part of your post. Sometimes covers are made months after the original. Sometimes covers are just fan covers (those can be good, sometimes).

Most covers I listen to tend to be relatively close in age to the original. But that's probably because of my music preferences.