With the exception of the headphone jack on the 1980's Yamaha A700 integrated amp, ALL of the amps I tested sounded VERY GOOD. What really sets the stage for the sound is the headphone itself, that has a MUCH larger impact on sound quality and "flavor." The better amps allow any given headphone to reach a tad more of it's full potential; and, especially with tube amps there is some "flavor" to the amp itself, though much less than the "flavor" imparted by the choice of headphone.
The one thing that REALLY surprised me was how good the headphone jack on the Sugden A25 integrated amp sounded. It's a good amp, sure, but I figured that since all integrated amp headphone jacks put resistors in series with the 'phones that this would so limit damping factor and other things that I would find it really objectionable. This was simply not true. While the Beta-22 sounded better than the Sugden headphone jack, it was an audible difference but not a HUGE audible difference.
Of course, there are some differences that don't relate to sound quality but to driving ability: the Bottlehead Crack could not successfully drive the LCD-2. And I just ordered a pair of HE-6's, and I expect that while the Beta-22 should drive these just fine, I really wonder if any of my other amps will have enough power to do the job.
Of course, I can connect the HE-6 to the SPEAKER outputs of one of my medium-powered speaker amps, like the Sugden A25 integrated or one of my other speaker amps: Monarchy SM70 (class A) - AMC-CVT 2030 a class A mosfet-EL34 hybrid, etc etc. And I will certainly try this. I already have a speaker-amp A/B comparison box which I use as a "passive preamp" and amp switch on my Quad ESL-57 speakers. I have two Alps stereo pots in this box, that allows me to set the gain for each power amp to produce identical loudness and then I use an A/B switch to switch the speakers from one amp to the other. I used this to select the amp I am using on those speakers- I tried a bunch of amps against each other. I found that due to it's more complex impedance load, a speaker has more interaction with various amps and this causes various amps to show more difference in sound than amps show with the simpler impedance curves of headphones. This is especially true with tube type speaker amps, the output impedance of their output transformer has a moderately strong interaction with speaker impedance curves, and I heard pretty large differences on speakers between a solid state amp and a tube amp. Some tube amps tended to produce a fairly bloated upper bass. For my ESL-57 speakers I settled on a Forte 4A amp. But sometimes I switch over to a H-K Citation II, which is one tube amp which didn't go all woolly on the ESL-57's. Anyway that's a digression.
So far my conclusion from this testing is that, yes, there can be fairly dreadful sounding things to drive your headphones with (Yahama A-700 headphone jack) but all the headphone amps I tried sounded VERY GOOD, with slight differences between them. To some people, slight differences could be important I guess.
NOTE: The Yama amp I'm talking about is a 1980's A700 amp, NOT related at all to the current Yamaha A-S700 product.