Before I became aware of LCPDFR, I role played a cop the same way most every other GTA fan did; I grabbed a police car and simply chased down, ran over or flat out murdered anyone I suspected of being a perp. I've never actually had a chance to play LCPDFR, but I do have experience at being a video game police officer in the form of True Crime: New York City. I can hear your collective groans as you read that previous sentence, but hear me out.
True Crime was, without question, a terrible game, but the police aspect was quite satisfying. You could pat down random pedestrians, answer call outs over the radio, collect evidence and decide whether you were a good cop or a bad cop, as well as turn on your lights and siren and blast down the street at high rates of speed for absolutely no reason, other than you have a badge and the other pricks on the street don't!
True Crime was unforgivably buggy, glitchy and often times just died during normal gameplay, but I have to admit that I spent far more time than I should have role playing a police officer, collecting my paycheck and buying new cars to upgrade and race around the streets. The only thing I feel True Crime was missing was any sort of traffic stop system. The cars would pull aside of you turned on the siren, but there was no pull over mechanic, the way there is in LCPDFR.
LCPDFR is amazing, and I hope to get the chance to check it out someday. A few years ago I actually picked up a copy of GTA 4 at a flea market, but since the game was sealed in a plastic bag I couldn't check to see if the code was inside. For $5 I took a chance and lost, big time! Now I'm out $5 and have an absolutely useless copy of GTA 4, but the only reason I even bought it was to try my hand at LCPDFR. LCPDFR detected I had a legit copy of GTA 4, but thanks to Rockstars system of DRM, I couldn't play either.