First of all, arrays are not pointers. This is an array of 10 doubles:
double a[10];
This is a pointer to double:
double *p;
This is a pointer to an array of 10 doubles:
double (*pa)[10];
And this is an array of pointers to doubles:
double *pa[10];
Arrays and pointers are only the same when declared as function arguments. But arrays can be converted (decay) into pointers to the first elemento of the array:
double a[10];
double *p = a;
double *q = &a[0]; //same as p
In your sample code:
double *x = new double[10];
You are creating a dynamic array of 10 doubles and getting a pointer to the first element of that array. You could also create a new array and get a pointer-to-array:
double (*x)[10] = new double (*)[10];
But this show of weird syntax is seldom useful.
About functions, this is a function taking an array of doubles:
void g1(double h[], int n);
And this is a function taking a pointer to an array of 10 doubles:
void g2(double (*h)[10]);
In the pointer-to-array case you need to specify the size of the array, because you cannot create a pointer to an unknown-size array.
That's why arrays are actually passed to functions as pointers. But pointers to the first member of the array, not pointers to the array itself. So the first function is actually identical to this one:
void g1(double *h, int n);
Since you only pass the pointer to the first member of the array (pointer to double) you need also to specify the size of the array, in an additional paramenter. The advantage is that you can pass arrays of any size. And even splices of an array:
double x[20];
g1(x + 10, 5); //pass x[10..15]
About which one is faster, they are both the same, they are actually pointers to the same memory address. Note that arrays are only passed by copy if they are part of a struct, and the struct is passed by value.
My recommendation is: if you use C stick to the idiomatic C, use pointers to the first member of the array when necessary, and avoid the pointer-to-array syntax when possible. If you use C++ use containers, iterators and ranges.