USB and Firewire are compeletely different kind of connections.
Dif plugs and dif protocols, not just a visual issue. The only way to make a USB to firewire connection would be using some kind of hubb with in/out connection to allow the input from one and the output via the other, but don't be mistaken because in the middle all the electronic circuits to make the transfer would be required.
In this kind of boxes you have to use the same out of the box that you use to input to the PC.
If the DVR records as Mpeg2 files it can have both or just one of them.
If the recording was made using uncompressed files you would need to use firewire.
However, if you have the chance to use firewire do it, because its more suitable to transfer the video files stream of info, doesn't depend on the I/O switches of your machine and will make less use of the CPU capacity.