Advantages of using MAMP stack over Mac's native Web Sharing and downloaded MySQL

I'd say unified GUI integration.

With MAMP, you've got a single window to manage Apache, PHP, and MySQL. Whereas with the built-in stack, you have to active PHP manually and have another interface for MySQL (with no easy way to turn it on or off)

The disadvantage is that you're installing stuff that you already have installed. This can cause problems when - for example - you want to use PHP using the command-line. This will trigger the built-in PHP version by default instead of the one bundled with MAMP. If these are different the results can be unexpected.

I would recommend using the default OSX versions of both Apache & PHP. After you got it all running the first time you really don't need a control panel or anything that much.