Scotts, the general rule of thumb is to go flat bottom wok for electric stove tops and round bottom woks for gas top. Round bottom woks also require a wok ring to support and balance the wok. One can season both iron and carbon steel woks, so they remain as nonstick as possible. CI woks are beastly heavy, as Kenny noted, and take a while to bring up to heat and they take their pleasing time to cool down. However, they do have the advantage of a more consistent temperature distribution along the whole surface, especially is you are cooking over gas or flame where the heat source is concentrated in a very narrow point.
Myself, I use the CI exclusively as it is very predictable, though there is a whole lot to be said about the lighter carbon steel. In light of what you say, for you, my arrogant opinion is that you need both-- a round bottom carbon steel (with wok ring) for your indoor gas stove, and a flat bottom CI for the grill.