Filtering $ n \times n $ Images by Separable $ m \times m $ Filters. Computation Time for Filtering Using FFT, 2D Convolution and Two 1D Convolutions
I'm not sure exactly what you're after, but just to try to add data:


Using the separability property of the filter is always the right choice.
Given it is separable we now have to apply 1D convolutions. Selecting which method to do it (Frequency Domain / Spatial Domain) depends on the length of the filter and the number of pixels in each dimension of the image.
There are cases where it is better to do FFT on the Rows and Spatial Convolution on the Columns.
This is all true when "Counting" FLOPS. Real life timing is more than that. for instance, if you're using highly tuned Convolution implementation and yet "Classic" DFT implementation you might be faster doing the Spatial way even for dimensions the analytic calculation predict it is better to be done in frequency domain.