Backlash in both acme and ballscrews depends on the nut you use, and not the screw. Typically acme nuts do have backlash. Most people buy anti-backlash acme nuts from dumpsterCNC - anti-backlash solutions for home and industrial linear motion
Be aware that these nuts are only zero backlash when the force is lower than about 25lbs or so. At higher forces, they will have some backlash.
If you're buying chinese ballscrew, most of them have very low backlash. Probably comparable to the acme with anti backlash nuts.