It really depends on the situation. If I am on the interstate with medium or heavy traffic, monitoring a long straightaway, LIDAR is clearly the best choice. It lets you target a single vehicle, and you can pick that vehicle up farther away.
If I am on a rural road with light traffic sitting just around a curve, I would prefer radar. When you target a vehicle with LIDAR, it takes a second or two for the unit to give a result (the intermittent beeps prior to the steady beep). So around a quick curve RADAR gives you a faster reading.
Our aircraft unit uses VASCAR. We get six or seven guys set up around a curve in the interstate, complete with orange signs and blue lights. Then the plane flies circles around three preset quarter mile courses, and the VASCAR calculates the offender's average speed in each of the three courses. The plane radios down to the ground units, and the ground units wave them over and write them. On one Sunday morning on a remote section of I-89, between 0800-1100, we wrote over $12,000 worth of fines (speed, following too close, marked lanes, road racing). To my knowledge, the aircraft unit has never lost a speed trial (except for lack of prosecution when they have to be elsewhere in the state).