Well, you shouldn't even be able to fly heavy bombers off of carriers, lol. Maybe in civ4 carriers will have a more accurate role.
For Industrial Age carriers, have them carry say 6 naval fighters, that carry torpedoes/bombs. Able to sink enemy ships, engage in air superiority roles, and carry out LIGHT ground attack duties, i.e. bomb enemy units in the open, and damage them only, no air to ground kills.
Modern Age carrier: nuclear powered, has 12 plane slots. 10 are devoted to attack planes, modern units that can be either air superiority units or fighter/bombers that can also engage in aerial combat, but are more capable at bombing and destroying land targets. Can kill some units, ruin infrastructure in cities, etc. The air superiority type craft should be able to engage planes before they get near the carrier, i.e. F-14s with Phoenix missiles, these planes should maybe have excellent antiship ability as well (Harpoons). The player can mix and match depending on what he/she expects to face during the campaign. The 2 remaining air slots CANNOT carry combat aircraft, but can carry antisub planes to protect the carrier, or early warning/control aircraft that can see enemy ships and planes at a long distance. Having one of these aloft could give your aircraft a bonus during missions. It goes without saying the modern carrier should have more move points than the early carrier.