Probably has something to do with the fact that in movies the actual car is being driven and doing the stunts etc. It's not a simulation of a car, and in GTA a pretty poor simulation unless their cars drive like 3 wheeled Yugos.
They probably don't want a game that has notoriously wonky car controls representing their cars as the handling etc will not be representative of the actual vehicle. This is a non-issue for movies as they use the real car, and less of an issue in Simulation style games like Forza and the GT series as they try to replicate how a car drives.
It takes a lot of work to get the details right, and car manufactures are probably pretty demanding on how their brand is represented. Forza and GT have entire teams that are dedicated to flying out and seeing the cars in person gathering all the data they can, test drives, exhaust sounds, suspension etc. That all costs a ton of money to do and they can afford it as it is the core aspect of the game. In GTA it probably isn't worth the money to spend the manpower and resources to gather all the car data. Not to mention the GTA engine may not be able to accurately use the data to the car manufacturers satisfaction. Which would require an engine redesign or update just to have accurate cars, which is probably not worth the ROI in sales for the game.
With Licensed Music you just license the master track, or a rendidition of a song, plug it in to the engine as the music while in the car and you're good to go. Don't have to record it all live or make sure all the instruments are accurately represented. Just license the song, get a hi-def MP3/ogg/whatever file of it and hit play. I'm willing to bet the ROI on songs is astronomically higher than the ROI on accurately modeling dozens of cars that please the licencors.