This is another subject where individual variances overwhelm generalizations. I can't speak to either of the two in question, but the three tube phono preamps I've had varied more in sonic "character" than the much more numerous SS ones, whose differences were mostly a matter of more or less "veiling". Many tube phono preamps are actually hybrids, with IC op-amp and tube stages combined. I believe the Project falls into that category; someone will correct me if I'm wrong.
My all-tube Fosgate Signature sounds better than any of the other phono preamps I've had, but it cost a lot more, too.
In the ideal world, the answer to your general question is "none". In the real world, the answer is "it depends".
Perhaps someone else can answer about those specific models.