Why would you want to find out what model you have? Well if you wanted to flash your xbox you need to know. The good news is you can find out the model of your xbox 360 dvd drive without voiding your warranty. There are three different models. First you need to look at the tray.
Benq OR Lite-On
If your drive looks like the last one it can either be a Benq or a Lite-On. This means you need to take off the face plate to find out (This does not void warranty). After removing the face plate look at the color of wires in the picture below (You will need a bright flashlight for this).
That is it! After knowing what type of drive you have you will be able to follow the right guide in modding your xbox 360. Happy modding!