Since I learned おまわりさん and けいかん I always wondered if the first has a "children language" nuance, or if it is just a friendly/respectful way to call a police officer. Is this the case?
お巡りさん is juvenile word for 巡査, which according to Wiki is the lowest rank equivalent to Patrolman. The kanji is a combination of 巡 = Patrols and 査 = Investigates. It would be acceptable in casual conversation or if you were friends with the cop, but not something I would call to the person responding to your 110番 call.
警察官 would address any person working for various departments of the Japanese Law Enforcement so you don't risk offending that person by not calling him by the correct title. If you wanted to be very polite, you could address the person (or group) as 警察の方 which should be acceptable in any situation.