Transistor amplifiers typically have a much faster slew rate than tubes. The slowness of tube amplifiers is mostly related to the rectification stage, though -- in older amps, a diode tube such as a 5AR4 or 5U4 is used, which can have a slew rate of 100 ms or more under some circumstances. Newer tube amplifiers typically, though not always, have solid-state rectification (usually 1N4007 diodes in a bridge configuration), which slew much faster.
Another characteristic of tube amplifiers that is of interest to musicians is harmonic content. Where a transistor amplifier simply takes an input sine wave and outputs an amplified version of the same wave, a tube amplifier will output dozens of harmonic waves as well. A "clean" sounding tube amp likely outputs a signal with 10 to 15% THD. A single-ended amplifier (one in which one or more output tubes simply increase the power of a signal) will tend to emphasize even-order harmonics (even-numbered multiples of the input frequency). An amplifier in a push-pull configuration (one in which two or more output tubes are paired, with each member of a pair amplifying one half of the input waveform) will tend to cancel even-order harmonics and emphasize odd-order harmonics (odd-numbered multiples of the input frequency).
A couple of weeks ago, I worked on a modern tube amp which was designed to allow flexibility in all of these areas. It had multiple stages which could each be overdriven separately or together for different overload characteristics, rectification switchable between tube and solid-state, and an output stage switchable between push-pull and single-ended. It even had multiple bias/plate voltage presets to allow use of multiple tube types in the output stage. Complicated, but kind of cool, too.
And the grandparent is correct regarding the gullibility of audiophiles. Anyone who would spend $60/foot on "premium speaker cable", when dollar-store lamp cord will conduct the same voltages and frequencies in an identical fashion should probably have their picture posted next to 'gullible' in the dictionary. =P