Both types of collet chuck can have the same accuracy when the diameter of the rod being held is the same as the bore of the collet. For every other size, the Beall or similar collet will be the more accurate.
The difference is that the typical MT collets are only split into 3 sectors, and from only one direction. That means that the jaws will change diameter only at the outer end as they are drawn into the MT. The result is a tapered inside diameter of the collet for any diameter other than that of the open bore of the collet.
The ER-32 collets that are used in the Beall and similar chucks are split into 6 sectors and in both directions. That means the collet will have twice as many gripping points, but also that the entire length of the hole will change diameter as the chuck is tightened. That means more grip, less chance to wiggle, and better accuracy.
Whether that is worth the extra money is a personal decision.