If you look at both the source code for System.arraycopy() of and Array.copyOf(), for performance.
System.arraycopy() is C code, it operates directly on your array, it does not return any values, and because of that it should operate much faster than Array.copyOf(). Nonetheless, if you need a new array to be created or if you just need the value of the copy operation then you have to create a new array for that, set the new array length, etc... Thus, you can't do a return System.arraycopy(source, 0, destination, 0, length).
For what Array.copyOf() can do then, it make a new array for you. You can assign the return value from Array.copyOf() to an array or returning it from a method as Array.copyOf() return to you a value instead of operating directly on your destination array. Thus, your code will look much cleaner. Nonetheless, for the cost of performance, Array.copyOf() is a generic type method and it does not know ahead of time what it will be working with. Thus, it has to call Array.newInstance() or new Object() and then cast it to the input's array type.
So to sum up. Use System.arraycopy() because of performance. Use Array.copyOf() for cleaner code.