I have no doubt the PureDAC's headamp is highly transparent, and this is why I use it perhaps 25% of the time for extended listening sessions.
My reasons for 'preferring' my tube amp are complicated. I tune neutral., i.e. I don't like syrupy, tubey sound. If there is a point of exaggeration, it may be that some tracks seem more dynamic, almost as if the Decware decompresses. Technically, it may be the response isn't quite linear and that rather than further compressing the dynamic range or faithfully reproducing the dynamics as mixed/mastered, the amp is expanding the range slightly. I'm no EE and this is sheer speculation; suffice it to say this is what it "sounds like" it's doing!
The other point is that without a doubt the amp adds even-order harmonics and puristically this is certainly coloration. However, all the music I listen to contains significant 2nd-order harmonics anyway. I don't listen to pure tones. I'm fairly sure my ability to distinguish the "pure Bosendorfer concert grand" from the "tube-augmented Bosendorfer" is pretty slim! The difference I think is likely to be subtle.
A third reason is the Decware Taboo sounded terrific before I bought the PureDAC. After, it sounded downright stunning.
The final reason: I tinkered with tubes a little when I was a teenager and I loved them. So, not surprisingly I actually like having a tube amp sitting in my room. Somehow, whether it is the ultimate in amplifier performance or not, the designer at Decware (and makers of other fine tube amps) succeeded in making something that sounds terrific. What's not to like?
WRT my comment about the Meier SS amp (the Classic), it too just happens to be an excellent amp. At present it and the PureDAC headamp are my "reference" when I make tube changes to one of the Decwares.
One of these days I plan to compare the PureDAC and Meier and decide which is 'the best'. I suspect it may be the PureDAC because of the advantages of BMC's 'pure' topology. This comparison awaits time and opportunity.
So I have had a new amp for a week now and I will say that I also prefer the BMC through my tube amp vs just the internal headphone out. My amp is a Red Wine Audio Cassabria, and it makes everything a little smoother and just more pleasant to listen to. Its actually just a hybrid amp with a FET drive stage but it definitely has a little bit more lively sound than the BMC straight. But, the BMC is really not far behind. I would be really curious to hear what a no-holds-barred headphone DAC built on the BMC topology would sound like (instead of being built to a price point, as Carlos said previously.)
Interestingly, my Alpha Dogs improve more with the tube amp than my LCD-3s. The LCD-3s are much smoother (but still seem more detailed) than the ADs. With the LCD-3 the change is more subtle but still definite. I have a few different tubes, some of which sound more "tubey" than others. The PureDAC does serve as a good neutral reference. At any rate, I could definitely have been happy to use just the BMC, but since I have this other amp, I will probably just keep it...