On the technical side, the Project Ember is a hybrid with a tube preamp stage and a solid state output stage (that one tube has two channels in it, ie, some OTL amps also have just one driver and one preamp tube, or one preamp tube), while the MkII is an output transformerless tube amp. The Ember will have less damping factor issues on low impedance headphone amps but the MkII will deliver more voltage into high impedance headphones. Now, given that high impedance cans (with the exception of really old headphones like the 600ohm K240) have high enough efficiency, a hybrid or SS amp can get 300ohm headphones like the HD600 much louder despite the lower output at that impedance range vs what an OTL amp can get out of a low impedance, lower sensitivity headphone like the HE400i or K702 given its lower output at 32ohms.
As for the actual sound, that depends. If the Ember is designed to be less of an amp and more as a warmifying colorifier, then it should be similar to the MkII, without the variable effects of how badly it will distort in either direction when driving a low impedance load. Or you can check the threads for it and see which tube will color the sound to what you like. Apart from the advantage of less risk with low impedance headphones, you only really need to switch out the preamp tube, and it uses only one of those, so that can be a lot cheaper for tube rolling.
So based on all of this, I'm guessing that the G1217 would be the better way to go since I will be driving K172 Pros (62 Ohms/105 dB) and Meze 99 Classics (32Ohms/103 dB), both of which are pretty easy to drive.
The Mk II appealed to me because it was an all tube design. I already have a Schiit Magni 2U which is kind of the opposite of "tube-y", very clear and true. An all tube design, I thought, would be what I was looking for as a counterpoint to that. Most of what I had read about hybrids is that they generally sound a lot more like fully solid state amps than fully tube amps. Would this not be the case with the Ember?