As a recent example, look at BF3. Installing on the HDD increases graphics/quality a lot, while other games only gain shorter load times.
You're right, but Battlefield isn't a good example. Installing the game with the install feature of the 360 itself doesn't change the graphics. The game looks always the same.
Installing the optional texture pack from the DVD improves graphics, but then it doesn't matter if the rest of the game is installed or not, both ways look the same ^^
As far as I know, Battlefield is the only game that has such a workaround where textures are installed separately.
Anyway, unless there is a optional texture installation the normal install feature doesn't increase the graphical quality. It just improves loading times and can help to reduce texture streaming.