Assuming you are running from a 12 V battery voltage, the efficiency difference is negligible. The LM2937 is a low-dropout regulator, which means it can be operated with a lower supply voltage for more efficiency, but when run from 12 V will be basically the same. There is also probably a difference in the current needed to operate the regulator, but that will be << 150 mA, so won't have much impact on the overall figure.
When selecting for automotive applications, there are other factors to consider. Temperature extremes are common, especially extreme heat. Vibration is another killer, and the electrical environment in a car can be pretty ugly in terms of spikes, surges, dropouts, and RF interference. Anything plugged into the car needs to be able to handle that.
Finally, remember current limiting -- normal bench supplies and wall warts are usually current limited to a couple amps. A car battery can supply 100s of amps, although you will presumably be plugging into an existing line with a fuse, that could still easily be a 20-30 amp fuse. If you use thin gauge wires, make sure it is protected by an appropriate fuse. What you don't want is a surge from the starter motor killing your regulator in a short circuit fault, followed by a fire in the wiring harness.