Off-the-cuff, and an objective viewpoint (yes, I know, sorry)... I am sure to forget a few pros and cons but here's a few quick thoughts.
Pros:
1. Impedance transformation; can take a high-Z (impedance), high-V (voltage), low-I (current) tube output and generate a low-impedance output with lower voltage but greater output current to drive cables and the amplifier load with less change in performance.
2. Ability to generate a differential (and balanced) output for greater noise rejection.
3. Isolation to reduce noise coupling and ground loops between (among) components. This also helps in the event a tube arcs and tries to apply B+ (high DC voltage) on the output; the transformer will prevent sustained DC on the output (but you'll still get a nasty pop).
4. Intrinsically AC-coupled (except for rare balun designs, and most tube preamps I've seen are AC-coupled anyway). This could be a pro or a con, I suppose.
5. Potentially simpler and less costly than adding an active buffer stage especially for differential outputs.
Cons:
1. Potential noise pickup by the transformer itself ( better line-level signal transformers are shielded to reduce this issue). Both LF hum and RFI.
2. Roll off of the highest and lowest frequencies (most good ones will have response well above the audio band; lowest frequencies may be an issue if you want sub-20 Hz output). Also introduces phase shift over frequency though likely inaudible.
3. High-level signals can saturate the transformer and lead to very high (and ugly-sounding) distortion. This can be a big issue for power amps, less so for preamps since signal power is generally low.
4. Stability; have to be careful in the circuit design to handle any feedback loops and watch for any HF ringing induced by the transformer's inductance interacting with internal, cable, and load capacitance. There is some load sensitivity but rarely an issue for a line-level stage (again more so an issue with tube amplifiers driving speaker loads).
5. Cost, though see (5) under "Pros" -- could go either way.
FWIWFM - Don
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