I have both and really like them both. They're quite different though. The ACC is a chassis designed from the ground up for PRS-type competition, if the main focus of your rifle is going to be competition, then the ACC is the way to go. Add the weights you need to get the balance and weight just right for you and you're off to the races. You'll end up with a rifle north of 20lbs though and imo, that limits your use of the rifle outside of competition. You can also run the ACC with no weights and even change the butt plate for the aluminum one from the ESS and end up with a relatively lightweight chassis. So although it's a "pure bred" competition chassis, it is quite versatile.
The XRS is a bit of a different beast. It isn't as optimized for competition since you can't tune the weights in the same way as the ACC. You can add a couple exterior weights and weighted butt pad spacers are coming so you can make it better for matches but it isn't as tune-able as the ACC. It is lighter though and quite a bit less expensive not to mention that if you hunt or shoot with it in colder temps, it's much nicer to be holding polymer than aluminum.
For what it's worth, my comp rigs sit in ACCs while I use my XRS for a long range hunter.