Advanced System Care like so many other system optimizers and registry cleaners performs 'fixes' on your registry which are considered risky.
For example they tend to remove empty registry keys believing them to be unused, when in actual fact some piece of software you run or the system comes to depend on that key, weeks or months later and of course when it's gone, it can cause errors or even crashing. For example a file extension keys are often removed, meaning suddenly you find you can't open those particular files by double clicking on them. And considering the way the registry is accessed, even removing 700 keys amounts to a next to nothing increase in performance and stability.
CCleaner on the other hand, in my experience, only removes so called 'safe keys'. For example, the registry key containing a path to an uninstaller, either the file that the path points to exists or it doesn't, and in the latter case, it's considered safe to remove. Though again, any speed boost or stability benefits are in nearly every case a placebo. It's an included feature because users want it, not because they need it.