My husband is a police officer. We have had lots of different detectors in our cars - I drive an SVT or an RX-8, he drives a Mustang GT, ergo, we drive in a "spirited" fashion. The detectors don't pick up anything if the radar is just idling, and most cops - if they're not lazy - don't keep the radar unit actively on all the time. It makes a horrible doppler-effect noise that helps the officer detect how fast the car is going - the higher the pitch, the faster the target. It sounds like feedback from an old radio - the whistling noise you hear in between stations. Most people don't like intrusive whining noises while they're working, especially if they're trying to listen to radio traffic. Lasers are mostly shoulder mounted rifle-type guns. They're expensive and bulky. There are fewer than 5 departments in our state that have lasers. You have to be sitting still to use them because they're not attached to the car and can't be calibrated for its speed.
My husband and I, out of curiousity (more mine than his) tested my detector (a Cobra, I think I paid about $200 IIRC) with the laser and the radar with me in my SVT and he in the patrol car. I was sitting in the garage, and he was parked in the driveway 10 feet behind me. He pointed the laser right at the car, pulled the trigger, AND THE DETECTOR DIDN'T MAKE A SOUND. I thought he hadn't pulled the trigger yet when he looked up and said, "Well?" Maybe it's a crap detector, sure. The radar worked from the rear, but not the laser. That was enough for me to not put faith in any detector. I took the detector out and haven't put it back since. If I get pulled over (and I have) I just apologize sincerely and hope the nice officer is having a good day.
A laser can tell a car's speed at nearly a mile away. If you can see it, the laser can tell you its speed. And it's deadly accurate. There's no fighting about which car was being targeted. Radar is much closer and harder to target. Usually when my husband flips it on he's within 30 yards. That's too close to brake and have it be effective at all. Even if they didn't get you in the second it took you to react, they're sure see your car nosedive. I know my husband laughs at people when they see a cop on the highway - people are such idiots!
Radar picks up "biggest closest fastest". So if you're in a Mini, and there's a semi next to you, chances are that the radar will be displaying his speed, not yours. But that's a chance you have to take if you want to speed. Radar has for a long time not been able to tell a car's speed going the same direction as the patrol vehicle. So if you were driving the same direction as a cop, you didn't have to worry as much. But that's pretty much obsolete now. They have all sorts of new technology, and one of the newest is same-direction radar.
This is all based on what I've talked to my husband about. I'm sure that there are other speed devices out there. But these are the ones that I know something about (not everything!) Hope someone finds it a little helpful.
EDIT:
Be nice to cops. They're just doing their job. You wouldn't like it if someone came into your office and called you all sorts of names just for doing what you're getting paid for. They put their lives on the line EVERY SINGLE DAY - for as little as $10 an hour. Would you risk your life for that? Most cops are genuinely good people trying to help YOU stay safe. They're not out to be jerks. They are bound by the law, and unless you give them a reason to pull you over, they can't. Smile and wave next time you see one in traffic. Give them the respect that they deserve!