The flat grind typically gives the best slicing configuration for a given blade thickness. It is also the weakest in a prying load. It is typically lighter for the stock thickness/width.
The sabre grind makes an angle much larger, which reduces cutting efficiency, but leaves much more weight on the blade, as well as giving it more strength when side loaded, due to the additional material that is still there.
The grind can be hollow to varying degrees. The hollow grind lets the knife keep a very thin edge farther up the blade. This makes for a very fine edge, and repeated sharpenings do not thicken the edge so soon. Due to the very fine edge, there can be very little steel to back up the edge, so the hollow grind is often used on fine cutting tools, rather than those designed to take abuse.
Obviously, these are all generalizations, and there are various things that can change them.
