I wasn't thrilled with either; I'd keep shopping.
Thought I should post again to clarify, so I dug out the knives so I could compare side-by-side.
The Ka-Bar Dozier is an OK knife. The action is smooth and the lock has a clean SNAP. But the pocket clip is an unnecessary annoyance, and the knife has a bit of blade play when opened. If I had a torx driver the correct size I might be able to remove the clip and tighten the pivot screw, I don't know.
The first Native is a sub-par knife. It's one of the 1st Generation BRK made by Camillus ($22). The fit and finish is not very good, there's quite a bit of blade play, the pocket clip is an eyesore, and the opening geometry does not feel 'natural'. Definitely a distant third choice.
The second Native is a newer VG-10 model, made in Japan ($30). As far as fit-and-finish, it's the nicest of the three knives. It's also the most expensive, 50% more. The opening geometry is no better than the older Native, but there's only the slightest amount of blade play. It's also much heavier and bulkier than the Ka-Bar, which could be seen as either a pro or con, depending on preference.
So as far as picking a favorite from the 3, the Ka-Bar Dozier is the smoothest and most natural, but the Native III is the best made.
A similar knife that you should consider, the AG Russell Featherlite. Better made than any of the above three and priced only a tad higher. It's also more interesting/unique because of the mechanism design, and it's more "pocketable" than the others.
Happy Shopping!
-Bob