there is no reason for cops to have greater capacity mags than civilians. They both have to defend against the same criminals. The cops have an advantage because they usually operate in teams. If they think they need 30 rounders, the people need 30 rounders for the same reason
There is a very small but genuine difference between cops and subjects, err, citizens. While we may only defend ourselves, our homes, and others in harm’s way, they are allowed to go on the offensive, chase people down, and storm fortified positions, and remove threats such as friendly Pekingese and terriers.
Cops may also be at a disadvantage in that way too many don't spend enough time at the range once they graduate from the academy and as a result, they are less proficient with a firearm than the civilian who carries.