The rules of engagement and comportment on paper are certainly stricter. I would be interested to see a survey on how the military handles crimes against civilians (whether American, host countries', or those within operational theaters) vs. crimes between soldiers or against the organization. There are several administrative and sub-legal tiers and provisions for punishing soldiers or modifying their behavior, but for the three classes of ligitative courts-martial, including the ultimate category of "general" court-martial which applies in cases of serious crimes and can deliver the death penalty, the conviction rates are at least as high as with civilian counterparts, being 90+%. It may even be that not enough cases go to the military courts after being 'settled quietly' or hushed up, but the justice framework itself is fairly robust after being reformed
following WW2.
So even if it's not enough, in practice and on paper it's stricter than what police are subject to.
One important thing to note about military justice (re: Rory's comment on enforcing similar structures or standards onto police) is that while it does incorporate civilian (federal) law, it has a legal structure of its own, which the Supreme Court has recognized as a "separate society" with distinct provisions and standards. So it may be better to assimilate police through legislation closer toward a general civilian model, rather than delineate another separate society when the conditions of war are so different from those of domestic policing.
*Interesting note on courts-martial: if the defendant elects to be tried before a jury of soldiers (rather than just the judge), the jury can convict on a 2/3 vote. Civilian juries of course must convict unanimously; a unanimous vote is only required in the military when the sentencing involves the death penalty.