Theoretically both of ways of calculating autocorrelation function are identical: strightforward convolution and Fourier-based method where we use FFT/iFFT in practice. And as it is well known, the computational complexity is $\mathcal O(N^2)$ and $\mathcal O(N\log N)$ for them respectively.
So the question is: are there any reasons why one could prefer convolution over the FFT-based method?
I could imagine only the memory-related argument (e.g. when we don't have any extra memory for calculations), but thinking of a regular PCs, at the time when memory constrains start to play role, the time complexity of $N^2$ will already be a killer for the first method.
Are there any particular numerical issue of the FFT that one needs to be aware of here (and choose convolution to avoid it)?