Overdriving your amp will make it distort more but not necessarily better. If you want to use the amp's distortion, you might want to change its "voicing" by placing an EQ between your guitar and amp input. Here's a small example of how a pre-distortion EQ can affect tone. In this SOUNDCLIP the first riff is without EQ and the second uses the exact same setup but with an EQ (mid boost) added between the guitar and the amp input. While it's not the greatest recording, it gives an idea of the effect of pre-distortion EQ. Why rely on the fixed voicing of a pedal when you can create your own with an EQ. It's an option that's seriously worth trying.
Of course, if you're looking for an entirely different distortion sound than what your amp is capable of, then do like Satch used to do. Use the clean channel of your amp and get your distortion from a pedal.