Sure, but one key difference is that if either of those groups steps outside the law, you can recourse to the law to check them.

Since police are part of the law, when they don't hold their own accountable, there's no recourse. And that's a real problem. This is before one even starts unpacking the knapsack of how much law is designed to protect the police from consequences of performing their duties (leading to the unfortunate example "They can blow the side off your house if they have reason to believe it will help them catch a suspect and the recompense is that your insurance might cover that damage.")