In your case, there is absolutely no different between the two. You cannot allocate the array dynamically (using "new" and "delete") with the second one however...
If you're asking about C++, the answer is neither. Use std::string x = "asdasdasd"; to store a character string.
Your first example is an error (formerly a deprecated conversion), which, if corrected, would have been written constchar* x = "asdasdasd";. This line creates a pointer called x, which points at the first letter 'a' of a nameless static array of 10 unmodifiable char.
Your second example creates an array called x and fills it with 10 modifiable characters (nine letters and a null)