Which way is better to create an array of fixed length in C++?

int a[N]; 

If N is not a constexpr, this is only legal under certain compilers, usually with language extensions enabled, or a C++14 compiler. ("Variable Length Arrays")

Note this is considered "C syntax" and the modern, preferred way to do this is:

std::array<int, N> a; 

This creates an array of N integers on the stack. If N * sizeof(int) is >= the remaining stack size, you may have a problem.

However: because it is a local object, it has automatic lifetime - it will go away when a goes out of scope. Allocating memory on the stack is also very cheap.

Second variant:

int* a = new int[N]; 

does not require MSVC+language-extensions nor a C++14 compiler, this allocates memory from the heap equivalent to sizeof(int) * N.

It does not get automatic lifetime - you will need to delete[] the memory when you are done with it. Allocating on the heap can be expensive, especially in multithreaded applications.

There may be cases where the memory needs of a program can only be determined during runtime. Then you should use :

int *A = new int[N]; //it's dynamic memory. Mean it can be change at runtime. 

Otherwise You should use :

int A[N]; 

compile-time array: C++ 11 has a new container named std::array, like boost::array, which is similar to standard container and can replace the traditional C array.
runtime array: vector is a good choice, you can reserve its size when created. other sequence containers can also be an array.

When N is very large you should use dynamic memory allocation otherwise it will give stack over flow exception.

Which is faster:

int A[N]; is faster because it can be stored on the runtime stack, and when entering the function it will just change the stack pointer by a larger number to allocate room.

int *A = new int[N]; is slower because you have to take the time to find a large-enough consecutive block of memory. Also, it is less likely to be on an easily-accessible part of the computer's storage.

For more information, see this related stack overflow question.

Which is better:

Regarding which one is "better" overall, it depends on the specific case. See this stack overflow question for more details.