You may get a cleaner, more balanced sound with a dedicated amp but it all depends on what sound you are after. The HD600 are pretty neutral in my book, so if you are after a bit more fullness and bass response then the high impedance powerful vintage amps will give you this. I used to have the Asgard 1 and I personally wouldn't pair it with the 300 ohm hd600, I think it is better suited with lower impedance cans, it was also quite a brightly lit amp. I haven't heard the Vali but I have read that it is a good match the Senn's. Most decent tube amps are. I also think that vintage amps with headphones are very much like tube amps... Only without the messing with tubes! I've never heard a modern SS amp sound tube-like. When I say 'tube-like' I don't mean 'warm' with low level distortions etc, It is the sweet treble and depth of image.
Because you are coming from vintage to a dedicated amp, you may very well be impressed with the sound. I went from dedicated amps to vintage and I've never looked back. But I love the sound of the 70's in general and am willing to sacrifice a completely black background for a smoother more natural sound (to my ears).
If someone asked me how I would feed the HD600- My answer would be tubes or vintage