Yep,
Not much difference. The NTK is such a design, where the tube is connected as a cathode follower, with four BJT's in parallel (thank you Gus!) as a load. The frame grid 6DJ8 is not exactly a tube for a microphone use and I was kinda surprised for this choice, but in this configuration its flaws (once again, as a microphone impedance converter) are probably not that prominent. Besides of NTK, the only use of this tube I ever heard is an EAR mic by Tim de Paravicini, (this guy always knows what he is doing). Anyway, in NTK transfomerless design the tube doesn't do much for a 'color', but serves rather as an idea of being "tube inside".
Change of capsule here will make much more difference, than a tube change.
BTW, it would be interesting instead of 6DJ8 (ECC88) to try to use Russian tube 6N1P. I am not sure if NTK power supply could handle almost twice as much of heater current (600ma vs. 375ma), but 6N1P IMHO is much better sounding tube and cost about $6.
But once again, I am not responsible for two things:
1) You blow your PSU because of higher filament current of 6N1P
2) Because of kind of schematics, you will hear any difference.