I like both.
There's one massive problem with hard-copy-only: paper burns. I work in an office where one group of people have paper-only files going back donkey's years. If there is a fire they are screwed. All those records are gone. If they had an electronic version of them, and and assuming it was reasonably designed, it would be searchable, it would be backed-up, it could be brought back on a DR site. As things stand they get none of that.
Despite that a paper copy is sometimes convenient (it's at least easier for me to read: the first thing I do when I get an important email that I need to pay attention to is print it). But the electronic copy is important.