My only experience with the AFCK/TSEK style of knife is my Mini-AFCK liner lock with the oval hole opener. So, keeping my very limited experience in mind, here are my thoughts :
If the knife is to fill a self defense role, I would forget the AXIS lock entirely. I believe Murphy's Law strongly discourages the placement of a lock release button in that location. (Just my unenlightened opinion.)
The large round hole is likely the fastest, most snag-free, safest, most reliable opener available on the AFCK/TSEK models. I think the oval hole is attractive but significantly inferior in operation, especially on the "mini" versions, where handling is probably more difficult to begin with. (Imagine a Honda Civic with oval tires.)
If the knife isn't required to fill a self-defense role, I would prefer the AXIS lock, and would rule out the AFCK because of that confounded oval hole and the black finish, at added expense. I would grab the TSEK and either learn to live with the thumbstud, or (far more preferably) remove the stud and make, or have made, a beautiful large round hole in it's place.
Remember, I know next to nothing, and although I find the artistic lines of these knives nearly intoxicating, the handle shape just doesn't work for me. I am probably part of a very small minority in that regard.
Dan