From the tenor of your questions, I suspect you're interested in the use of a cathode follower vs. an output transformer to drive a low-impedance load, like the 600 ohm input impedance of a classic compressor. The short answer is that a cathode follower, by itself, won't do that.
Here's the story. 600 ohms is low enough that you can't drive it from the plate of a tube; it loads down the tube way too much, the gain drops drastically, and the distortion skyrockets. So you use, say, a 10k:600 ohm tranny, and now the tube's plate sees a load of 10k, which it can handle (if it's a nice hefty tube like a 6SN7). The cost, however, is a 12dB drop in signal level from the stepdown transformer.
So why not just use a cathode follower? After all, it has an output impedance around 600 ohms, right?
Well, not exactly. A cathode follower can be thought of as a voltage amplifier with 100% feedback, so that the gain is unity. (Actually a little less, but we'll ignore that.) While you're bringing the gain down, the output Z also comes down, so the output impedance is lowered as well.
Now load the tube with 600 ohms. The feedback...uhh, WHAT feedback? The 600 ohm load has brought the open-loop gain of the tube down to virtually nothing, leaving no margin for the feedback to reduce the output impedance, clean up distortion, etc.. So a cathode follower feeding a 600 ohm load has a very low clipping point, high distortion and a high output impedance. Bad news.
The good news: a cathode follower does a fine job at the output of a mike preamp if it's feeding reasonable impedances, like 10k. (It's still unbalanced unless you do some maneuvering, but that's doable.) I use one in my Big Mike preamp. But it won't work into 600 ohms. To do that with tubes you need a stepdown transformer; pity, but 'tis true. (For those interested, I cribbed this explanation lock, stock and barrel from Norman Crowhurst's "High Fidelity Circuit Design", which is available in .pdf form at the
http://www.pmillett.com/technical_books_online.htm site.)
Even then it only does a fair job. The problem of providing really clean outputs into a 600 ohm load, with high headroom and low distortion, is remarkably difficult. Some things, I hate to say it, are easier to do with solid-state, and this is one of them.
Peace,
Paul