I don't really know if they are a LOT more efficient, but I prefer the solid connection when pushing hard. I do pull up on the pedals sometimes. When I occasionally ride without cleated shoes, I have to pay attention to keep my feet on the pedals.

I prefer to buy my shoes locally, though I have occasionally taken a chance on buying a pair online when it was a really good deal. I have found a huge variety in the actual sizing and comfort, so it's worth a little extra to be able to try them on.

I ride with MTB shoes. My "road" shoes are a pair of Specialized Sport Mountain shoes, which are styled similar to the road-only version except for some tread on the sole. I also have some Shimano MT-22 MTB shoes, which look more like normal street shoes and are comfortably walkable for longer periods. I wear these when I am expecting to be on and off the bike.