Quilt batting would generally be used to polish the water and will have a very high density.. i.e nothing much would pass through.
Poret foam will have lower density, so using a graduation will allow your mechanical filtration to work throughout it, and have the water go through large then ever decreasing pore size, so it will allow flow for longer, and require less frequent cleaning too.
I believe there are bacterial benefits too, even if you just rinse and reuse the batting.
Batting is much cheaper though.