They now have private police instead of a quote public police with different rules and who is keeping the or recording the numbers?
How do you arrive at the "different rules"? I'm pretty sure they are using the same criminal code and folks they cite/arrest are being brought in front of the same courts as the old force did.
Sure, the protections afforded by the Constitution against certain government behavior do not apply but the liability for both civil and criminal response to the actions of individual employees as well as the parent company are far greater. As an example, screw up a citizen's arrest and see the hoo-hah fly. Write a speeding ticket based on a radar gun that was not both properly calibrated and said calibration not reported to the state and watch the hoo-hah fly. From what little info was there it iseems to be a private security company acting as a private security company, not as sworn law enforcement officers.
Virginia has a somewhat similar discussion going on
http://forum.opencarry.org/forums/showthread.php?129216-Hmm about Special Conservators of the Peace, which for all their faults are given court commissions that somewhat limit their behavior and reach.
And the saving of taxpayer money? Sure, if you hire a company that pays around $15/hr plus limited health benefits as opposed to whatever the former force was paying its officers there ought to be a significant savings.
stay safe.