The interface is slower, but the drive might be faster. It really depends on the drive in your computer. If it is a laptop, an external 7200 rpm drive will probably be faster, but otherwise, no, your internal drive will be faster due to the peak transfer capabilities of the drive interconnect.
Firewire 800 has a peak transfer of 100 MB/s, sata either has 150 MB/s or 300 MB/s, so the firewire interface is slower, but the drive speed is what limits all of these technologies right now.
Firewire 800 is probably not going to be faster than SATA I or SATA II (1.5 - 3 gbps). It might be faster than PATA.... But I'm pretty sure that at this point, as I've said in many other threads, single hard drives are not capable of matching the interface speed anyway, so you will not see substantial improvements. For instance, when you take a hard drive in a FW400/800 enclosure and test 400 vs. 800 (where you should theoretically get close to a doubling of speed), you only get a 20% increase in speed. Why? Because the hard drive cannot sustain cache-to-interface transfers at 800mbps anyways.
EDIT: To sndcj1's point, I am talking about using the same hard drive. His/her point is certainly valid, that if you pair changing to Firewire with getting a faster drive, the result may be different....
Yes, with a fast external HD you'll get better performance that with your laptop internal 5400rpm HD. If possible I would also go for a 800-compatible one if you are all into performance. Like was said on a post above, the speed increase 400 vs 800 is something like 20%. Haven't messured this myself, but thinking that could be pretty accurate from what I have experienced myself.