I have both and like both but there are differences. The 350 is wider and thicker, the blade steel sharpens nicely and holds a great edge.
The 566, in my opinion, fits the hand better. It is slimmer and less wide. The steel is also very nice. It too holds a great edge.
My 350 opens a bit quicker than the 566. There is also a sound difference as the blade hits the stops. The 350 has a sharper sound. I think it is due to the liners/G10 scales compared to the steel liner of the 566.
Both, again in my opinion, are very good EDC knives...at least for me living in Northern NY where it seems most people carry a knife and have more guns per household than any other area in the North East...I'd expect to get "looks" from people in more "liberal" or "civilized" areas.
I could not recommend one above the other except for how it feels in the hand and the 566 fits my hand better thought the 350 was not a problem.
I've had no problem sharpening the 350 using the Lansky system...I prefer to reprofile my knives when I get them and had no problems with the 350.