I don't have an X-Surf, but I have network cards in my three main amigas, and I don't use them
But to be honest that is because I have never got everything nice and stable.
For transferring files I use: CF-Card (and micro hdd), Jaz and Zip drive, CD. I find CD is what I am using most often, because it is easiest. Also, I occasionally move hard drives between computers.
I think AlexH has a good point. Think about what the end result is that you are trying to achieve. There might be other solutions.
But if you're like me, and really enjoy mucking around with things, fiddling, setting stuff up, and then not using it, a Network card might be just the kind of toy you need