let's consider ai infinite and flat sheet of charge distributed on a conductor. Well, it is known that the electric field at steady state on its surface (which is orthogonal to it) is equal to:
$\ E = \frac\sigma {2 \epsilon} $
where $\sigma$ is the surface charge density.
Now let's consider the specific case in which this conductor is a perfect electric conductor. Let's apply the interface conditions for electromagnetic fields, precisely for the normal component of the electric field (let's call 1 the space inside the conductor and 2 the space outside it):
$\ D_{2}-D_{1} = \sigma $
So, since the internal electric field is 0 in a perfect conductor, we get:
$\ D_{2} = \sigma $
that means:
$\ \epsilon \cdot E_{2} = \sigma $
Finally:
$\ E_{2} = \frac \sigma \epsilon$ that is double with respect to the field evaluated with the first method.
Notes: as stated in the reference of the first method, the conductor electric field is double than that of a simply sheet of charge (without speaking of conductors). But I have seen, for instance, people apply the equation $\ E = \frac\sigma {2 \epsilon} $ to find the E fild inside a parallel plate capacitor (there is also this evaluation in the reference). In this case, the plates are conductors, so why do not we use $\ E = \frac\sigma {\epsilon} $?