I've found that one of the things I listen for in a good tube amp is its noise floor. It's not necessarily something I do on purpose, as a critique, but more it's just a show stopper for me. If I hear any hum, it reminds me of a guitar amp or an old low-fi tube console system from the 50's. It ruins the experience for me.

Tube amps can have a rich full midrange that's hard to beat. But they can also have a deep black dead silent quiet between passages. That's important to me. It enhances the impression of realism.