On this question, you might want to check an article on GetAndroidStuff called Superuser vs SuperSU. Quoting:
SuperSU improves everything about Superuser and adds more options. The free version offers faster notifications, there is possibility of disabling them for each app and a new interface, attractive and easy to handle. In addition, according to developer claims by using SuperSU you’ll enjoy higher speed from the apps that require root rights, especially on Android 4.0+. The paid version called SuperSU Pro provides the opportunity to keep root rights after a system update, which usually cancels these rights. Although the method is not guaranteed the option is very useful. We have password protection and advanced log configuration settings for each application.
You might also want to read SuperSU Brings Better SuperUser Root Permission Management to Android. Quoting from that article:
SuperSU is basically SuperUser on steroids. According to the developer, it “allows for advanced management of Superuser access rights for all the apps on your device that need root.”.
ChainsDD versus ClockworkMod
As I initially missed you were not asking about SuperSU, but ChainsDD versus ClockworkMod: Let's take a look at AndroidPolice:
- Koush's SuperUser is free and Open Source
- Sources are available at Github
- it supports JellyBeans (4.2+) MultiUser (SuperSU does this as well)
- it will never have a pais version, which would go against the whole open-source principle
- like SuperSU, it makes use of the new
android.permission.ACCESS_SUPERUSER permission (already used by several root-apps)
- PIN Protection
- Request Timeout
- Customize notifications
- x86 and ARM support
- tablet optimized (Koush speaks of "tablet mode", so no fear it wouldn't do on a phone :)
Read more in the linked post at AndroidPolice.