Grand Theft Auto 5: PSA #2

Told you I would get to it...

So while you can also install the play disc to the hard drive it is strongly recommended that you do not. While Rockstar hasn't posted the official reasoning yet the 'wild ass internet guesses' suspect that the ability to read from the HD and the DVD simultaneously can increase data transfer rates.

Also from Rockstar Support:

For optimal performance, we recommend only installing the Install Disc, and not also installing the Play Disc to the Xbox 360 Hard Drive or USB drive via Xbox Home (dashboard). You will be prompted to install the Install Disc the first time you boot the game.

Joystiq posted a video demonstrating what can happen: