pros and cons:
online (i don't use this service, so i'm guessing a bit):
-access from virtually anywhere (with an internet connection)
-most places are secure and stuff
-don't have to worry about data being lost or maintainance, since a good online company will make their own backups etc, especially for paying customers
-good internet connection + fast =
-need a good fast upload speed to backup to server
-big files, as mentioned = long time. same applies to any sort of data transfer.. therefore maybe/maybe not feasable. if small files/total files then i guess its fine..
-no instant access to it when you're offline.
-bad/no internet connection/slow = :-/
usb hdd:
-in a location you/someone can access (instant access). also be able to access it without going online
-plenty of software that will create scheduals for backup (even windows), and restore that backup
-you can specify how big a drive you need, how people access it etc.
-big files is no problem, due to a cabled connection (network/usb/firewire/esata) it loads faster in/out etc.
-does get hot, but that can be resolved with air-con or a cooling implement to aid it. good hdd case design is always a bonus. same with having the drive not stored in a major heatspot
-you do need to maintain and take good care of it, as well as having a contingincy plan incase your backup hdd starts to show signs of death.
-if it has valuable data on it, you may want to use some encryption on it, or at least lock it up with a kensington lock/safe. (since its physical thing, it could get stolen or something bad)
-need a home to stay on your desk/cupboard/store room/safe/etc.
there's probably a lot more pro's and cons to it, just a few i can think of the top of my head. Like nodsu said, it depends what kind of data you're gonna be backing up. Say if its a whole image of a PC hdd, every 1-2 days, then obviously online's not gonna be much use to you.