Should I use `rand % N` or `rand() / (RAND_MAX / N + 1)`?

I was reading the C FAQ and found out in a question that it recommends me to use rand() / (RAND_MAX / N + 1) instead of the more popular way which is rand() % N.

The reasoning for that is that when N is a low number rand() % N will only use a few bits from rand().

I tested the different approaches with N being 2 on both Windows and Linux but could not notice a difference.

#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#define N 2

int main(void)
{
    srand(0);
    printf("rand() %% N:\n");
    for (int i = 0; i < 40; ++i) {
        printf("%d ", rand() % N);
    }
    putchar('\n');

    srand(0);
    printf("rand() / (RAND_MAX / N + 1):\n");
    for (int i = 0; i < 40; ++i) {
        printf("%d ", rand() / (RAND_MAX / N + 1));
    }
    putchar('\n');

    return 0;
}

The output is this (on my gnu/linux machine):

rand() % N:
1 0 1 1 1 1 0 0 1 1 0 1 0 1 1 0 0 0 0 0 1 0 1 1 0 0 0 1 1 1 1 0 0 0 1 1 1 0 1 0 
rand() / (RAND_MAX / N + 1):
1 0 1 1 1 0 0 1 0 1 0 1 0 1 1 1 1 1 0 1 0 0 0 1 0 0 0 0 1 0 1 1 1 0 1 1 0 1 0 1 

Both alternatives seem perfectly random to me. It even seems like the second approach is worse than rand % N.

Should I use rand() % N or rand() / (RAND_MAX / N + 1)?