Why do tube amps often subjectively sound more powerful than SS ?

It's not really about loudness, it just feels more powerful at the same volume.

@inna, Mapman has it right. The reason the tube amps sound like they have more power is because of how they make distortion when approaching full power. Unless its an SET, with most tube amps the higher ordered harmonics start showing up in greater amounts near overload. This interacts with the ear which imparts the impression that its louder- more powerful. This has given rise to the false notion that tube power is more powerful than solid state.

But like @mapman pointed out, if you have a sound pressure level meter, you'll find that its not louder- and in fact might be quieter.

I mentioned the caveat of SETs- they take this to an extreme by producing those higher ordered harmonics at a much lower power level- perhaps only 20-25% of full power, which is why many people talk about their 'dynamics' (since power is used the most on transients). But what they are really talking about and also in this case is distortion and how it interacts with the human ear (the ear uses higher ordered harmonics to gauge sound pressure).

Tubes make it an enjoyable experience since there's plenty of second order harmonics to go around too.

I mentioned the caveat of SETs- they take this to an extreme by producing those higher ordered harmonics at a much lower power level- perhaps only 20-25% of full power, which is why many people talk about their 'dynamics' (since power is used the most on transients). But what they are really talking about and also in this case is distortion and how it interacts with the human ear (the ear uses higher ordered harmonics to gauge sound pressure).

You've mentioned this before, and I finally got to experience & hear this phenomenon for myself. Spot on. Push-pull amps are better for me, especially since I like to listen loud. 

Put simply and without a lot of technical detail, as other have noted, many solid state amps sound downright nasty when they clip, while tube amps don't. That allows you to leave the tube amp at the higher volume even though it is still clipping versus a clipping solid state amp that sends you running to turn the volume control down.  That's one of the big reasons many electric guitar players greatly prefer tube amps.

I swap in a 250watt/ch ss amp with my 45watt/ch tube mono blocks. I leave the volume control on the preamp at exactly the same setting for both amps, as the volume in the room from the speakers is identical. 

I listen mostly at moderate levels, not much distortion besides the one coming from the recordings themselves and some from the speakers that I do hear.

The impression is that tube amp does have more power in reserve, and you can feel it.

Tubes are superior to transistors, anyway, and that's a true explanation ! I agree with many others here.