The only reason to use Apache is that it’s easier to get WordPress to do whatever-they-call pretty URLs with Apache. I’ve been using Apache to reverse proxy a sub-folder site for over a year and haven’t yet had a reason to change, but I’d probably recommend NGINX if you were to ask.
Edit: Oops. I read too fast.
Oh. If it’s a separate install then I’d go with Apache since that’s what WordPress “likes” better. I’d probably just go with DO’s one-click WordPress installer (I’m assuming that there is one).
If they are on different servers, then it doesn’t make any difference whatsoever. Do the easiest thing, which is to install WordPress on Apache.