I think they are about as different as two headphones can be.
The Teaks have massive sub-bass and mid bass slam (to me; a non-basshead), have almost no isolation, and are not particularly fast. They have recessed mids, that are still high quality. The mid-bass can overshadow the mids. If I recall correctly the mids and treble measure with significant distortion. The overall listening experience is great though as it's very smooth and coherent. Very V shaped. The sound stage is very good for semi-open headphone. They are not particularly comfortable until you get a Pilot pad and I use the ZMF Eikon pads. Then they are fine. I prefer them out of the Jotunheim and balanced using a periapt cable. I think the current version on Drop has a fixed cable again.
The AFC is somewhat polarizing. Some people love them while others can't stand them it seems. They are very neutral and have mildly elevated sub-bass and mid-bass (slightly above neutral). They are very fast, with very clean mids and treble with fast transient responses. The sound stage is smaller vs. the Teak. Comfort is excellent. Noise isolation is very good.
Neither are suitable for portable use IMO. The Teaks will fall off and don't isolate. You can drive them with a phone or DragonFly Red, but they don't sound that dynamic from those sources. They really do well with the Jotunheim (excellent synergy). The AFC needs a lot of power to sound good. I've tried them using a DragonFly Red and they sound thin with no dynamics or impact. Even with the iFI iDSD micro they don't sound dynamic enough for me. I think they need a Jotunheim/Lyr 3, etc. level of power to start getting dynamics and bass.