The Toshiba T-3400 and T-3400CT are basically the same computer, with different screens. The 3400 is monochrome, and the 3400CT is active-matrix color. The 3400CT is also slightly larger, heavier and has a shorter battery life than the monochrome version, but not by much.
The Toshiba T-3600CT is apparently just a 3400CT with a better CPU, RAM and harddrive. The color screen on the 3600CT is slightly larger than that of the 3400CT. It didn't come in a monochrome version.
The T-3400[CT] has these basic specs:
And, the T-3600CT has these basic specs:
I have had almost no trouble with Linux's interaction with my 3400. The only thing which seems a bit odd is that every once in a while, it'll drop all keystrokes for about 2 seconds. This isn't really a problem as much as an quirk. I don't recall the problem exisiting with Windows/DOS, but then, it only ran Windows for about a week before I had time to purge the infection and install Linux.
My current best theory on why this happens is that it has something to do with the hard drive parking its heads. I've noticed that there is a little thunking sound when the keystrokes are being ignored, which I assume is the hard drive parking after a specified period of inactivity. I have no idea why this should effect anything, but it seems to.
Update: It turns out that there was a bug in the keyboard BIOS, which is what caused the dropped keystrokes. Replacing the motherboard is the recommended cure for this, but I never could convince my warranty shop to do it (the just reflashed the BIOS, which had no effect) -- so now that my T-3400 is out of warranty, I just live with the problem.