Portable amp compatibility will depend on what version of the K340 you have. If it's a bass heavy version, then you may very well get away with it since you'll still have a full sound with relatively good tonal balance.
A bass-light K340 absolutely needs tubes. It's not neutral, it is very much on the bright side, so you need a warm syrupy amp to balance it out. Also, it is extremely revealing, so if you plan to use it portably with an mp3 player as a source, forget about it. You need a resolving, transparent, and grain-free source or you will clearly hear all of the problems.
Of course, that is only for the bass-light version I have. It is downright painful with Hornet/X5 but very lovely out of the main Rega/MG Head rig.
As far as comparisons to other headphones go - honestly it depends very much on the version you have.Comparing a bass-light K340 to the SR-404 shows that the Stax does have superior microdetail, a larger soundstage, and more bass extension, but in every other regard I think the bass-light K340 is superior. It has a much better midrange with slightly emphasized lower mids, a very linear though boosted treble, and a very tight, punchy, well-controlled bass. There is something very solid and authoritative about its sound, which the Stax lacks. It does get a bit shouty at times, and compared to something truly world-class it is a bit coarse, but given how dynamic, musical, and yet detailed it is I can forgive it that. Definitely one of the best headphones under $1000, even better than the HD600 which under the right circumstances can be one of the best headphones ever made. It just has that "magic" that I look for in a system yet have the Devil's own time trying to define, even if it is a bit rough around the edges.
The stock bass-heavy version wasn't nearly as good, but I can't give detailed commentary since my exposure to it was brief.
