Most of the tone difference is related to how a Vacuum tube Audio amplifiers handle overload. Basically you can beat them to a bloody pulp, and you are unlikely to damage them, and unlike solid state amps, it really doesn't mess up the sound quality very much. Most vacuum tube amps that were rated for say 20 watts RMS output could in fact delivery 200 watts peak without either damaging themselves, or producing the really gross distortion you'd get from most transistor amps.
Unless you run a transistor amplifier in class A operation, some level of distortion is unavoidable because of the inherent non-linear characteristics between 0 and .6 volts.
(If you run class A, you never get down that low, the device is always 'on'). Technical and economic considerations preclude the making of 100 watt class A amplifiers for anyone who cannot afford his own biz jet!
If you want sound quality, generally you are going to want a tube radio with push-pull output, and nothing smaller than a pair of 6V6's running class B (that will give you about 15 watts), 6L6GC's will give you about 30 watts. After that you start looking at big power tubes like 811's.
IN any case look for a power transformer, and a pair of identical tubes next to a second transformer (audio output transformer).
If you find a 50C5 and a 35W4, you are looking at a classic 'All America 5', serviceable yes, Hi-Fi, forget it. The main claim to fame with the All America Five was that it didn't need a power transformer (which made it cheap to build). Most 4 and 5 tube radios are All America Fives, or a variation. (The Variation is often the 35W4 rectifier is replaced by a solid state rectifier, and the 35V drop is provided by a combination of dial lights and/or Glo-bar droppiing resistor. For example the Heath Kit Low end shortwave radios like the GR91 are exactly this variation of the All America Five design and added an Isolation transformer for safety. The bad news is the sloppy hobbyist who worked on an All America Five was likely to get a shocking surprise, if he wasn't electrocuted! Generally one side of the chassis was connected to the line cord, so if you were lucky, it was connected to the neutral, if you weren't, well... (and these are much older than polarized plugs!)..
Purists will insist on class A, but class A has a maximum theoretical efficiency of 25% (and the desire for ulta linearity and practical consideration generally limit it to 20% or so, so for any reasonable power output, you are actually buying an electric heater for the room.
If you over drive a vacuum tube amp , they become non-linear, but unlike solid state amps, they won't 'flat top' which produces horrendous distortion products, and or blows the fuses to protect the transistors. Most transistors won't tolerate even short term gross overloads. By contrast, there are vacuum tubes that were actually designed to take short term overloads of 100000% (yes a 1000x overload, such as an Eimac 4PR1000A). Most garden variety tubes will tolerate 1000% overloads for a fraction of a second without any damage at all.
Ones you buy used at this point usually need some work. The electroyltics in the power supply have generally had it, and many of the other caps are suspect. These are analog devices, and drift with time, so it is usally necessary to re-align the front end and IF strip. On an AM radio you can generally do it by ear. On an FM radio, you are going to need an oscilloscope and a sweep generator. Most are in fact 'stagger' tuned to provide the required bandwidth for FM.