what makes a tube sound the way it does?

Tubes are used a lot in recording studios for miking and also for mastering....that pleasing tube sound can improve a "thin" sounding mix...it can also act as a limiter to reduce dynamic range on a studio mix in a very elegant way. Studio miking with solid state can prove to be a challenge due to the shear dynamic range involved...as already mentioned a tube amp recording a mike will clip nicely if the sound goes out of range whilst a SS amp will sound awful as it clips....so tube amps offer advantages if you don't get the gains correct or the mike is placed too close to the instrument.

OTL (Output Transistor-Less)

There are scientific reasons tube based equipment will sound different to the human ear. First, a tube plays about 4 times louder per watt than solid state. A tube's harmonic distortion occurs on an even order as opposed to solid state devices where it occurs on an odd order. And yes, when tubes approach clipping, they are more "rolled off" than solid state equipment. Also remember that with tube equipment, one can use different brands and types of tubes which can affect sound quality. If you are considering a "single ended" tube amp as opposed to a "push-pull" type tube amp, you will want to consider a high efficiency speaker. Like with anything else, there are good and bad tube based equipment. Look for a well established manufacturer. There are a lot of "garage" made equipment that probably should be avoided.

I also have a tube preamp, and I have been wondering the same thing. One set of tubes can sound different than another set of the same type.

To me it seems that this happens when the internal construction is different, that is, the plate, terminals, heater, etc. are rolled or shaped differently.

These differences would affect capacitance mostly, maybe inductance also. I guess that could explain the differences in sound.

Or maybe the emitting electrode has a "terroir", the electrons having a kind of audible flavor based on where the metal came from. This seems less likely, but who the heck really knows?

As to tubes vs solid-state, compensation circuits may play a role. Transistors are very non-linear devices, and even differ from device to device. Bias and compensation circuits are used to make circuits that work the same way with different transistors, and to control the operating nonlinearities and extend the linear performance range. These circuits are actually feedback loops. And feedback can cause non-harmonic distortion that sounds bad. For example, a transistor's gain actually changes depending on the current going through it; a compensation circuit would introduce some current somewhere in the circuit that dynamically compensates in some way so that the gain looks uniform at the top "black box" level, but really there is a non-linear feedback loop in there. And there are more loops like this than you would think.

Tubes, on the other hand are already pretty linear, and it's pretty easy to test them and find matching sets. To make outstanding equipment of either kind you need to be a design wizard, but it may be that a decent transistor amp might be harder to design than a decent tube amp.

Also, negative feedback in the amp design could be a source of difference. Transistors and tubes respond differently to NFB. In particular, NFB in transistor circuits reduces the lower number harmonic distortion but not the upper, in effect emphasizing the higher distortion harmonics, which sound nastier. Tubes are more tolerant. Again, this is an area where transistors are harder to tame.

Yet another reason for differences is in the input/output characteristics at the top-level circuit. Electrons don't know inputs from outputs, they just go with the flow, and will as lief go in the out door as out the in door. Interaction between the input and output circuits is hard to eliminate or predict (given that there is no standardization of I/O circuits), and tubes and transistor have very different behaviors.

So, there are plenty of reasons why things should sound different. The more I learn about it, the more impressed I am that they sound as good as they do.