Microwave: A microwave heats water and molecules in the food by using microwave radiation. It will heat food efficiently and quickly, but does not brown or bake like a conventional oven.
Oven: Fueled by gas or electricity and heats from the bottom (baking, roasting) or from the top (broiling). The heat is from a single direction and not uniform.
Convection Oven: An oven that has a fan that circulates heated air. This allows for operation at a lower temperature while cooking more quickly. It also results in a more even bake.
Convection Microwave (Oven): A combination of a microwave and a convection oven. Allows for even, quick cooking that is browned or baked.
So, at the bottom of the scale is a microwave and an oven. They each have different functions. Then there is a middle tier that would be a convection oven - an improvement over the oven. The top tier is the convection microwave oven that provides all the features: quick cooking, heating, baking, browning, and evenness.
If you do a lot of cooking and only have a single oven, but find yourself wishing you had a second, a convection microwave would be useful for you. If you want something truly multi-purpose, then yes. Since each has a set of features it provides and/or lacks, it comes down to what best fits your needs.