By sequentially transmitting whole directory trees? FTP-the-protocol never had anything useful to say here. It's always been about FTP-the-client and these didn't need things like "control channels" and "active mode" to do what they're doing.
FTP is a pretty conceited protocol, and one that deserves to go away. People say it made more sense in the 80's, but I was there and even then *NIX/Solaris admins found FTP to be about as much fun as that IRC pingback identd service; which is to say not very fun.
I tried implementing WebDAV servers some 10+ years ago. Back then this was a major pain with different clients expecting and sending different properties etc. No idea how this looks these days.
I think I last tried it four years ago or so. Not much had changed. I briefly used Apache as a server; I think the server was fine, but the open source clients were flaky at best. I also used to have a hosting account that included WebDAV support, among others, but I never got any client to work with it except for the web interface bolted on top of that thing.
I'm surprised to see WebDAV mentioned here, to be honest, I thought it was a dead horse everywhere except in enterprise.