Let's start with the knife that's more well-known. The Genesis is a true virtuoso performance, in my opinion. Well designed, well executed, well-finished, smooth action, innovative clip.
What the Axis and Pinnacle both have on the Genesis (and Commander) are that neither use a liner lock. I have seen problems with Emerson's liners occasionally first hand. I have not noticed them in the Genesis, but I have not had the opportunity to really look yet. The fact is, liner lock problems abound. Most people don't know how to test for them; on top of that, a liner lock that passes all tests can suddenly begin to fail.
If I were carrying two folders, most assuredly at least one -- and preferably both -- would not be a liner lock. Right now I don't carry any liner locks regularly anymore.
Okay, annoying sermon over.
Archie, I have a feeling that you'll be happy with any of the Axis, Pinnacle, or Genesis. The Axis and Pinnacle both have recurved blades, which are harder the sharpen than conventional blades; if you're a novice at sharpening, you should definitely start with the Genesis instead. In addition, both the Axis and Pinnacle are "unproven" at this point, though I have a feeling both will prove to be exceptionally well-done. The Genesis is a proven, rock solid design, and even with my dislike of liner locks, I think you'll be thrilled to pieces with it.
I don't have any of the above 3 knives, but my first purchase will definitely be an Axis. Genesis is also very high on my list. They are in that order because I already have a well-proven liner lock in my collection (M-2 AFCK), so my top priority is a top-notch non-liner-lock. Last priority for me is the Pinnacle, partially because I just ordered a Sebenza. Again, the Genesis is awesome, the two Benchmades probably will be awesome also.