Which of the two pieces of code returns a more accurate answer?

Question

So, I am trying to return the square root of a number in two ways, which in my view are not so different. Which of these would have a higher accuracy and why? As far as I can tell the second would be the better one, as I believe the default "allowed error" (not sure how that is called) is much lower than my set variable 'eps': 0.00001. Is that correct? Does this have to do with Codeblocks or the compiler or the processor itself?

First method :

#include <iostream>
using namespace std;
int main()
{
    double a,b;
    double x;
    cin>>x;
    int nr=0;
    //double eps=0.00001;
    a=1;
    do
    {
        b=a;
        a=(b+x/b)/2;
        nr++; //used to keep track of number of steps made
    }while(a!=b);
    cout<<a;
return 0;
}

Second method would be the same, except for the do...while() condition:

#include <iostream>
using namespace std;
int main()
{
    double a,b;
    double x;
    cin>>x;
    int nr=0;
    double eps=0.00001;
    a=1;
    do
    {
        b=a;
        a=(b+x/b)/2;
        nr++;
    }while(a-b>=eps || b-a>=eps);
return 0;
}