IEEE1394 is referred to by the Apple name "Firewire" most of the time, as well as "iLink" or "DV port" on video devices. It's a transfer protocol, similar to USB.
1394a is the format since 2000, and transfers data at up to 400 megabits per second. This is the one most devices currently use, including DV cameras and DVD recorders.
1394b is a newer version, allowing up to 800 megabits per second. I've not really seen any "b" devices to date, not even for external hard drives or DVD burners.
USB 2.0 is up to 480 megabits per second. While this sounds "faster" than 1394a, it's actually a slower sustained datarate than the Firewire. This is why you won't see USB on digital cameras or video devices, which require better sustained data transfer rates.
Some more advanced info is available here:
The only advantages that can be gained are if your hardware device requires that soft of connection (meaning your computer must use that type of Firewire or USB card for max speed). While IEEE1394b and USB2.0 devices will run on the slower predecessor connections, it will be at the reduced speed of the predecessor.
I would be surprised if you have any Firewire "b" devices.