What determines good distortion?

This is a really old question.
SS amps tend to clip 'hard'. They really have a flat top to the clip waveform, and thus create really strong high frequency output when clipping. (what that is, and means to a layman is too complicated for me to enlighten you, get a book on amplifier disign)
A tube amp clipping creates rather 'soft' rounded clips,(way less high frequency junk being created) and thus are gentler on speakers.
So, in general, the tube clipping is way more survivable, and rather 'easy' on both speakers and ears.
The SS amp will clip and sound grating and harsh, besides killing your tweeters.

So neither of you are 'wrong' You just have different experiences.
Yes clipping is bad. Yes a tube amp will be able to clip and be less problematic for both hearing, and tweeters.
So you are both right.
And he may just like the sound of tubes... which is his right in general.. Then you have those who say 50 tube watts are 'bigger' than 50 SS watts...

But I bet neither of you usually run the amp so hard they produce clipping anyway. So why worry?

Some solid state amps have clip protection. Such amps produce a waveform smoothly limited in the same way as a tube amp. Also, mine is good for 600 watts, so I don't think I need to worry.

What I've always heard is that SS produces odd order harmonic distortions (3rd,5th, etc) while tubes produce even order distortions (2nd, 4th, etc). I've also heard that musical instruments produce even order harmonic distortions, which is why most folks find tube equipment more "musical" or "natural", because it's distortions are more similar to that heard from a musical instrument.

J, I think you are mistaking tube for single ended and ss for ultralinear. An old Pass Aleph does not distroy even order harmonics like an old ARC push pull.