A cycling shoe with a stiffer sole is always better, regardless of the type of bike you are riding. I have several fixed gear bikes, some for long distance non-stop riding, and others for urban riding with some time walking. I use serious carbon soled cycling shoes with road clipless pedals on the former, and walkable SPD shoes or regular shoes with straps on the latter. I also use my stiff cycling shoes on my serious geared road bikes.