It depends on the game. Generally the reason for running a game from its default installer is to save memory. Some installed games will reboot your Amiga and run the game without loading Workbench, therefor making them installable and playable on stock standard 2MB systems or whatever they were designed for. WHDLoad-installed games will require more memory because usually you'll be running Workbench in the background, and even if you write a startup-sequence to load the game without Workbench, it'll still need to load WHDLoad in the background, which can be enough to run out of RAM for some games.
The advantages of using WHDLoad to install the game are many though. First, you get a quit key, so you can exit back to Workbench at any time during the game. Several patches can be applied to the games. Many can be forced to NTSC, which is handy for games that have that huge black box at the bottom of the screen. Often there are options for unlimited lives/ammo/credits or whatever. Fixes can be made to games that had bugs in them, keys and buttons can be remapped (very handy when a game uses UP to jump and you're using a control pad with extra buttons). All these options (depending on the game) can be accessed via the icon tooltypes of any WHDLoad-installed game.
One more thing I'll mention, some games still require certain a disk to be in the floppy drive when the game is installed or they won't run. (For example; Super Stardust, Super Street Fighter II, Mr. Nutz I think). WHDLoad fixes this! It's now possible to run Super Street Fighter II on an unexpanded CD32 for the first time ever (since the commercial CD32 version was never released) thanks to WHDLoad.
