The claw method is the best way to play. The biggest reason being that you can easily perform frame perfect aerials, while maintaining full control of your DI. The only drawback with this method is that it is really difficult to learn.
I don't know how it affect most characters, but for Falcon it is a huge benefit. Frame perfect rising knees and uairs can hit a standing fox. With full control over your DI and timing of your aerials, you will be able to combo with deadly efficiency.
There are other ways to get these benefits though, one way that I know of, is using the lower part of your thumb for the c-stick, while using the tip of the thumb for X/Y. #SwaggarNation