ParNet is faster than serial transfer; over a network is better over all but damn near impossible if you are connecting to a PC using Win 7. CF cards and USB drives via sneaker-net is quick and easy (vs CrossDos). Samba supports most OS's, but not with Win 7. Google "idiots Guide to Samba on Amiga."
Personally I never got connected to my Win 7 PC and I either directly download to my Ami or sneaker-net with a USB drive; I have a 16gb thumb and a 320gb HDD. There ought to be a USB-to-USB way of doing this, but I haven't found it; there are Ethernet "crossover" devices to go computer to computer via the Ethernet port -- haven't done that yet either:)