According to this Gamespot article, Microsoft’s supposedly seen a 30 percent improvement in load times on games installed to the 360 hard drive, although no direct source is given. From the article:
One of the not-so-cosmetic changes in the fall update will be the ability to let you play your games directly from the hard disk. The new feature will let users install all of the game content directly onto the hard drive to improve game load times. Microsoft reports that it has seen a 30 percent improvement in load times in internal testing. As an interesting data point, Microsoft went out of its way to tell a group of reporters that the full Devil May Cry 4 hard disk installation took roughly 10 minutes on the Xbox 360. The installation took twice as long when we conducted our own installation tests on the PlayStation 3. Another side benefit of having games installed on the hard disk is reduced noise, since the optical disc no longer needs to spin up. However, you will still need to have the game disc in your optical drive while you’re playing it, presumably as a piracy check.
More through the link.