Periodogram seams to be one data point short on the frequency axis. Thus the frequencies are incorrect. With an input vector of length n, I think the periodogram should have n / 2 +1 points.
The example I have should have a peak at frequency 0.2. Instead the peak is at 0.203. The input data is 30 cycles over a length of 150.
Scaling the frequency axis by DataRange -> {0, (n / 2 -1) / n} seams to give the correct frequency.
Compare with Fourier, plotting 0 to 1/ 2, which is n / 2 + 1 points.