What are the pros and cons of Convection Microwave Ovens?
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.