It's a bit of a misnomer to talk about a distinction between convolution and FFT. By the convolution theorem, the two are mathematically equivalent. In addition, on paper, FFT-based convolution scales much better than traditional convolution because it reduces the complexity from O(n^2) to O(n log n).
I haven't done the benchmarks for a fully optimised implementation, but comparing naive implementations you can easily tell that FFT-based is much faster (even with all of the tricks that MATLAB does to optimise sparse matrix operations).
I haven't done the benchmarks for a fully optimised implementation, but comparing naive implementations you can easily tell that FFT-based is much faster (even with all of the tricks that MATLAB does to optimise sparse matrix operations).