Being playing with "well tempered" tuning today, no real difference for me but still kind of nice to have it anyways. Just curious, if it is noticeable and important for the rest?

I very much hear a difference. Certain parts of the diatonic chords work and have character.  Others don't.  So if I were to use tempered tunings I would need to use them more carefully. Since it changes chord progressions in ways that make each pair of chords in a progression much more individualistic.   So if its worth effort for the particular case I might set up multiple pianoteq instances and use them tuned so that parts of the progression can be, for example, equal tempered, and other parts (or specific chords) may be in a well tempered or pure tuning.  So I can see why someone playing modern music, with the more involved chord progressions, would not be able to necessarily appreciate the imparted character of well tempered tunings. 

Mostly I just go for pure tunings once in awhile, on only certain chords. And use 12 ET (12 tone equal temperament) for the rest.

My advice to newbies of such things (which you certainly are not) would be to select a pure tuning first, and let one's ear learn to understand how it relates to 12 ET. 

Pure minor thirds sound a bit more uplifting whereas 12 ET minor 3rds are much more melancholy.

To me Pythagorean Major thirds sound a bit brighter, just a little on the "manic" side, relative to the 12 ET versions, whereas to me Pure Major thirds are more balanced and reserved.  The thing is, to me if I use a Pure tuning in a synth it definitely sounds awkward, unnaturally stuck, like a held standing wave.  Natural music has movement (call it imperfection but I say its just movement...)  A more correct tuning application, than what presently exists, would IMHO, allow tunings to adjust relative to beat.  For instance, I might want to gradually purify a chord, or use a Pythagorean triad tastefully to add its brightness, but not have it remain constant.  This would need to be carefully done, but since I'm a guitarist I can bend the strings of a chord in real time and test the principle in some cases (although I can only bend certain things this way - I would like the additional flexibility of a software dynamic tuning approach, if someone would get around to this.  I imagine in 5 or 10 years someone will do it.

Thanks a lot, very refreshing to me. Interesting, I did not know about closer - farer tonalities behavior. Will go check it now. Maybe it could be interesting idea to play some pieces in WT but with base tonality tuning shifted to the main key of a certain piece. Need to figure out how to do it in Pianoteq settings.

AKM, this is exactly what I do when I want to play in unequal temperaments such as WT.  Open the Advanced tuning pane, and in the right column, use the the +/- buttons to adjust the scale to the tonality you are playing in. It doesn't work so well for pieces that are more chromatic, i.e. use a lot of accidentals, but it can sound wonderful when the tune has a pretty consistent tonality.

I think that our ears are now so used to equal temperament that using, let's say WT tuned to C, to play pieces in wildly different tonalities and hoping that each tonality will have its own "color" doesn't really work (it doesn't for me at least). When I think of Chopin's Preludes, written in 24 different keys, I wonder which temperament his piano(s) were tuned to. Nobody knows for sure it seems!

I would be thankful for some feedback (sorry for my German accent)... ;-)

All temperaments are compromises, one way or another. ET compromises by making all keys very slightly out of tune, but all equally so. So playing in C major will sound just as good as F-sharp major, as far as "being in tune" goes. The various "well temperaments" compromise by making the simple keys (C major and those close in the circle of 5ths/4ths) more perfectly in tune, but as you move to keys away from C they become progressively more out of tune. Some people like the "color" and variety that the various states of out-of-tune keys gives, but by the time you get far from C (along the circle) things can get VERY far out. Again, different temperaments compromise in different ways, so some more perfectly tune C major, and so F-sharp major can be way out, others make C major just a little bit out which makes F-sharp major a little less unstable.

And yes, composers long ago very much did avoid keys with more sharps/flats because of temperaments used. By the late baroque temperaments were more sophisticated. Still, Handel famously had an organ built with "split black keys" where the lower half was tuned down and the upper half was tuned up (basically two keys in one). This way he could play in keys with more sharps/flats and stay more "in-tune." As "well temperaments" became more refined, it allowed playing in all keys without sounding too bad as you moved to F-sharp... hence Bach's "The Well-Tempered Clavier" which cycles through all 12 tonal centers. As temperaments more favorable to the remote keys became more common, composers experimented more and more with modulation and wrote more regularly in remote keys.

Anyway, all of that is a gross simplification of temperaments in musical history, but it generally explains the progression.

As a general rule of thumb, if you're playing in simple keys, earlier temperaments can sound nice. As you play music with more remote keys, ET has clear benefits, unless you want to embrace that idea of the various colors you get out of non ET temperaments. Again, they are all compromises, but to me, ET is one of the most fantastic compromises ever devised.

Thanks a lot, very refreshing to me. Interesting, I did not know about closer - farer tonalities behavior. Will go check it now. Maybe it could be interesting idea to play some pieces in WT but with base tonality tuning shifted to the main key of a certain piece. Need to figure out how to do it in Pianoteq settings.

And yes, composers long ago very much did avoid keys with more sharps/flats because of temperaments used. By the late baroque temperaments were more sophisticated. Still, Handel famously had an organ built with "split black keys" where the lower half was tuned down and the upper half was tuned up (basically two keys in one). This way he could play in keys with more sharps/flats and stay more "in-tune." As "well temperaments" became more refined, it allowed playing in all keys without sounding too bad as you moved to F-sharp... hence Bach's "The Well-Tempered Clavier" which cycles through all 12 tonal centers. As temperaments more favorable to the remote keys became more common, composers experimented more and more with modulation and wrote more regularly in remote keys.

Anyway, all of that is a gross simplification of temperaments in musical history, but it generally explains the progression.

As a general rule of thumb, if you're playing in simple keys, earlier temperaments can sound nice. As you play music with more remote keys, ET has clear benefits, unless you want to embrace that idea of the various colors you get out of non ET temperaments. Again, they are all compromises, but to me, ET is one of the most fantastic compromises ever devised.

Play a C4 together with an E5. Equal sounds ugly, Well temperament sounds fine.

Very clear difference indeed. So, I mean, I'm genuinely curious so besides this spots what it gives us practically, say, as a performers? I kind of got the idea but would like to hear it from someone else :)

I guess there are other combinations that are ugly in WT but fine in Equal? Did composers deliberately avoid the "ugly" ones? Like Bach, Haydn, Mozart, Beethoven? How about a tradition of transposing the Baroque music in the times written, widespread to my understanding?

In equal temperament, play a C major chord, then an F-sharp major chord. Then switch to a non-equal temperament and repeat the same two chords. The difference should then be very noticeable.

Not so much regarding the sequence of chords, but C major triad by itself definitely sounds slightly different, I'm able to hear it. I mean that if I play, say, Chopin or Bach be it Equal or WT I don't feel like something wrong or better. I would never notice listening to, say, Richter playing, whether it is WT or Equal.

-edit-
My bad, F-sharp, not F. Sure, it sounds very odd to my ears in WT.