Gigabit ethernet generally faster than Firewire 800?

In general, GigE should be faster than Firewire 800. There are some variables at work that may make FireWire faster, but except for Ethernet congestion from other traffic they're edge cases. If you're looking to connect more than 2 hosts, Ethernet is by far the better choice.

Gigabit is in much faster unless you provide it via a slow expansion method such as PCI. Firewire is only 786 Mbits, but if you have significant traffic on your network you could conceivably get higher speeds from firewire.

In general you should do whatever is easier for you, since the raw connection speed of both technologies is fairly similar.

If you already have a gigabit network set up, don't worry about creating a new firewire connection. If you don't, maybe (Macs for example) Firewire is easier. But all that depends on your environment and the kind of software/hardware you use.

More specifically, the absolute transfer time for your file depends not only on Firewire vs. Ethernet, but also on the protocols. With Ethernet you'd usually use IP. But with TCP or UDP? TCP is good for unstable connections, while UDP has less of an overhead. Even if you decide on TCP, Windows file sharing, just as an example, works rather well if you want to transfer lots of small files, whereas FTP is pretty good at transferring fewer but larger files.