We have both...for good reason.
Our dogs make great alarm systems...larger breeds and loud barks at ANY stranger who dares get close to the house.
Our cat is a great mouser...this is somewhat luck, as not all cats are.
We live in a rural setting, so both cats and dogs have a use...if you don't have a mouse problem, I can't really see why a cat would be necessary though.

To me if living rural, both.. for the very reason's Denob said.. Dogs for alarm, dogs for tracking, Dogs for marking, The perk and joy of a good dog is that they are smart enough, change the equipment and change the training.. example, put a pack back on my guys and they are pack dogs and we are hiking.. put a harness on and its tracking, put a certain type of collar on and its work the farm critters etc

but honestly good farm cats are important, mice, moles and rats and flying rats all do so much damage.. my farm cats earn their keep..