This is a very common but quite loaded question, given the mythology surrounding the subject.
Ultimately, categorization of amps into "solid state" and "valve" or maybe a third "hybrid" category may not be that helpful in describing the sound, since the performance characteristics will really depend on the design and construction of particular amplifiers, no matter what kind of parts they use. In practice, a lot of tube amps are designed in a certain way and may share some characteristics, so there are some trends, if not much more than that. In general, if you want a cleaner, less modified sound into most headphones at a lower price, solid state options have significant advantages. If you want to try something else, then all bets are off.
One of the best posts I've seen about this issue is this:
For a better answer, you may need to define "bring out the best sound" more carefully.
Edited by mikeaj - 3/5/12 at 2:57pm