I haven't done a direct comparison myself, but you have already stated that it depends on the filter size. You also mentioned that the PS has access to some texture filtering instructions that aren't available to the CS - but will you make use of filtering operations? It sounds like you already know quite a bit about the difference between the two shaders, so you just need to apply that to your specific needs and see which one is needed.
By the way, there is a separable bilateral filter implementation available in my Hieroglyph 3 engine in case you want to start out there. I would be interested to hear what choice you make on this topic!