If you're batch sparging, then a SS braid would be cheaper and would IMO work just as well.
If you're fly sparging, then nothing can beat a false bottom.
I have a Listermann's plastic false bottom for a 5g cooler, and a SS false bottom for 10g.
The Listermann's has slightly smaller diameter holes, and I get a clearer run off with that than with the SS one, but that is probably (as Parker36 said) because I have a greater grain bed depth to filter the grain rather than the smaller hole diameter.
The downside to the plastic one is that it is much easier to get a stuck sparge, and requires a lot of attention to detail to prevent this.
I prefer the SS one to the plastic, but to make a realistic comparison, I need a keggle so I can do 10g batches, or a 5g size SS false bottom for the smaller cooler.
If anybody wants to donate said items, I'd be happy to write up a comparison.
-a.