FWIW this is all about distortion. Solid state amps have a harshness due to trace amounts of odd ordered harmonics (5th and above) that the ear uses to sort out how loud a sound is. It is because of the latter fact that the human ear is very sensitive to these harmonics, and so even though they only show up in trace amounts (as far as our test equipment is concerned anyway) we hear it as harshness and brightness, even though the amp has a flat frequency response.
To get detail though you have to get rid of distortion, as the ear's masking principle means that distortion can block the presence of detail. This is why tubes are still here some 50 years on after being declared obsolete. They don't make those odd ordered harmonics in such great quantity, and so sound smoother.
You could say and rightly so that tubes more closely follow the rules of human hearing in this regard.
Now tubes can get bright too, like transistors, if you use a lot of loop negative feedback in the design (this is BTW one reason that transistors are bright- most transistor amps use feedback). Although feedback gets rid of some types of distortion, it does not do everything. This is because the amplifier circuit always has a propagation delay, a small but measurable length of time it takes for the signal to propagate from input to output.
Because of this the feedback signal is always arriving a little too late. As frequency is increased, this problem is exacerbated and results in trace amounts of odd ordered harmonics, which it is *supposed* to be getting rid of. You could add even more feedback, but you would need more gain in the amp to do that- IOW the carrot will always just slightly out of reach.
For this reason the smoothest sounding amps potentially will be ones that don't employ feedback.
When looking for smoothness and transparency, another way of describing this is linearity. When an amplifier is linear, it is low in distortion. But if it is to be low in distortion and lacking feedback, it will have to employ other techniques to keep distortion at bay.
One of these techniques is to use linear devices in the signal chain. Triodes are immediate and obvious choice. Another design feature that has long been known to be more linear is the class of operation- the most linear known is class A. Further, if the amp is fully balanced and differential throughout, it will be lacking the even ordered harmonics for which tubes are often faulted. Since these lower ordered harmonics usually have a lot more energy associated with them, they can obscure more detail although they add 'warmth'.
So there is a short list of features to look for- good luck and have fun!