A lot of hard cases will not cover the top and bottom because the case has to have some give for it to fit. I currently use a Spigen hard case for my 5S that does cover all sides but it has little slits at all corners so it can go on and off properly.
I used to use a Power Support Air case for my i5 that covered all sides and had no slits. It was my favorite case ever but a little pricey and hard to put on and off, but worth it.