At QuakeCon last year we resorted to using LanShark, and it worked out great. I think one of the reasons why is because the name was easy to remember and spell
T_T I can'y imagine trying to tell someone "Yeah, go download aybabtu. that's A-y-b-a-... I'll email it to you."
If you are on a wired network, or can wire each to a shared network I've had great luck with lanshark on windows PCs to transfer huge (60+gb) steam games from friend's computers to avoid downloading them after purchasing.
It may appear to freeze when copying large numbers of files and even bring up a "program is not responding box" it is. Just leave it for about 10 minutes and everything should become responsive. You can open up task manager and see that your network and disk is being used. The UI just becomes unresponsive when beginning huge transfers.
If you don't have a thumb drive large enough you could use winrar to break it up into rar parts and just move a few at a time. If you are not on the same network I would just get a couple of cheap 32gb thumb drives and literally mail them. Your home connection probably doesn't have all that great upstream.