I only recently started my tube amp adventure, and I (subjectively, without measurement) hear quite a difference to a non-tube amp.
The thing I like about the tube amp is that I can wilfully introduce distortion to get a sound that is different, unique, yet still pleasing to my ear.
A "clean" tube amp makes little sense to me, there are simply better alternatives, both in technology, longevity and price point.
I enjoy a holographic, breathy sound that I'm hearing. It lacks punchy bass and bass control, it's by no means perfect amplification, but it gives me the idea that it's more lively, or maybe "live" as in I hear the same distortion characteristics when hearing a live band play in a bar (with their own over-distorted tube amps usually).
As for tube rolling, I have limited experience so far, but I can imagine different sound characteristics might have more to do with the wear and tear (storage condition, as a lot of tubes said to have "characteristics" are old, and from areas like the former USSR, and burning hours) of different tubes than actual consciously implemented differences by a manufacturer.
To me, it's not subjectively better or worse, just a different experience that I equally enjoy.