Having heard both of them in 2 different setups :
CEC TL51XR > Stax SRM-717 > Stax Omega II
Lavry DA10 > DIY Pass Aleph > AKG K1000
I can say that I would choose the OII over the K1000 here but that's not quite fair since the Stax setup is more expensive. I don't know how would the Omega II behave with a lesser source than the CEC but I believe that they're really source AND amp dependent, very sensitive to every upstream components. The K1000 is kinda like that too but it isn't as refined as the Stax, they're too much distant for me, lacking some body and bass, which the OII, don't lack at all and that's quite a feat for a stat if you ask me. The Stax grabs you smoothly while the AKG let's you fly in the air at a cost.
Hope it helps, I can't comment any further cause I don't own any of these and only had so little time to audition each cans.
My vote goes for a KGSS + OII setup !