I also prefer a Stabilizing System that offers a more fine tuneing friendly design, as in the Carbon Impact Multi Carbon Rod with the tuners, and the Beiter Stabilizer Multi Rod with tuners, fine tuneing for best balance in the hand, balance after the shot and the optimim vibe and noise dampening.
I also look for a stabilizer with a quick disconnect knuckle for my 10 inch to 24 inch Stabilizers , for the ease of fitting into a hard bow case.
I also like to have a stabelizer that I can work with a V-BAR bar or side or rear weight system. As well as said by others a stabilizer that will allow me to add screw in weight at the front of the stabilizer, although the Carbon Impact Multi Carbon Rod Stabe I am using as of now is tipped with a Simms Limbsaver and I really like that feature, it performs extremely well.
For bowhunting also I look for a Stabe that will withstand a bump against the tree on the way up on the bow tow rope and not be damaged, I am always banging mine against the tree, also looking for a stabe that will withstand the abuse my eqipment takes in the field and still perform flawlessly.
Looking for simplizity of use with durability and maximum nose and vibe dampening with the option of adding weight and system bar accessories, V- Bar connector that can be added with the option to ajust the V-Bar positions by angles.