Different things
FireWire is the general standard used by digital audio and video equipment, so it's the better bet to interface a camera.
Independent from that, I do not believe that the fact that you used USB to transfer your video altered it in the way you described - that's what I ment: Just because you took a different way to transfer your video, you still transferred the same video. That is the very point of digital media - there is no deterioration in copies.
I think it's pretty improbable that USB mangles your video where FireWire wouldn't, however, if the video on the camera/disk/tape is truly better than the one you transferred, the only explanation I could think of is that you didn't actually
transfer it, but
re-rendered it. (That's actually not so far-fetched.)
If that is the case, you have to find the encoding options for transferred videos, and either set them to higher resolution/bitrate/whatever you desire, or, if possible, to something akin to "same as source". If your camera's documentation tells you the parameters of your recording, you could also manually set it that.
Mind that, if you're really re-rendering while capturing (as said, not that far-fetched), you'll have to make a trade-off: More compression vs. bigger file size. The more compression you use, the crappier the video will look, and the less useful it is for further post-production. The less compression you use, the bigger your file becomes (we're talking gigabytes here).
You could also try capturing/encoding into a different codec. Especially MPEG-4 based codecs (DivX, XviD, Quicktime) look far less "blocky" than earlier MPEGs or other video codecs, but they're not as widely supported in video editing programs.
The very best you could do is transfer .dv/.dif, the native recording format of the camera (assuming it's a MiniDV one). However, I'm not sure that option is available in normal consumer products - I think it's more likely your program encodes AVI.
Either way, bottom line is: I don't think it's the method of transfer harming the video...either your camera mislead you, and the video didn't look that good in the first place, or your capturing software works against you.
If in any way possible, it'd be best if you checked capturing on a different computer. If the result is the same with different hardware, you can assume it's not USB messing with you.
Out of interest, what software do you use to get the video from the camera?