We've heard a lot of arguments in the past three pages, but the only poster who evidently has experience with this is Sansloi36, who posted on the first page- he served on an aircraft carrier for several years, and thus, his suggestions should be considered more heavily than the rest of us armchair admirals.
I'm in San Diego visiting relatives right now, and in San Diego harbor there are two carriers- the USS Midway, built in 1945 (and refitted in the 60s), and the USS Ronald Reagan, the Navy's most modern carrier.
The differences couldn't possibly be more striking. The Reagan can carry more, is faster, has longer range, and has markedly better defense systems. The need for an upgradeable carrier in BtS is very apparent, as the current model represents a WW2 age carrier, not modern nuclear-powered supercarriers.
Even though carriers are now better in BtS, they're better because other features have been nerfed, not through their own power. And naval combat in Civ4 is already so unrealistic that this minor change for the better doesn't have enough impact to suitably change things.
As someone mentioned, in every modern crisis, the question is "Where's the nearest carrier?" In the naval battles over the past 60 years, you see an overwhelming number of pictures of carrier-based planes attacking ships, not battleship confrontations. There's a reason why the US hasn't built battleships in decades, but continues to turn out massive supercarriers...
In Civ4, things are absolutely reversed. The battleship rules the seas, and the carrier is only there as a support unit. In BtS things have been made a bit more realistic, because there are actually missile cruisers in modern times and again carriers are relatively more powerful, but you still rarely have battles like the ones that happened in history: Midway, Leyte Gulf, Coral Sea, Rolling Thunder, Desert Shield, etc.
It's completely unrealistic for aircraft not to be able to destroy ships: In real life, fighters don't just 'damage' the enemy and wait for the surface vessels (counting historical precedent, these vessels would most likely be dozens of miles away). Admittedly this would have a balancing efect, but as someone said before, that effect would just be countered by everyone paying more attention to naval aviation and less to battleships (I can't think of a single battle since mid-WW2 when battleships were used at all...)
The argument shouldn't be over whether carriers should be intrinsically powerful, because it seems like the vast majority believe that the carrier is a transport, not a fighting unit in itself. Carriers just don't fulfill their realistic role in BtS, and that doesn't make sense, since there's no balance or other reason for them not to do so.
Regarding the questions of individual carrier power, it does have merit that a carrier would have things like first strikes, improved recon range, and so on. However, this should be based on the number of fighters aboard- therefore, I'd propose that a carrier gains 1 first strike chance and +1 visibility range per fighter aboard (giving regular carriers a maximum of 3 of each, and supercarriers 5-6 or so). The first strikes wouldn't be a huge influence, and I believe that first strikes don't count into strength calculations for which unit gets attacked first in a stack, so it wouldn't make carriers more vulnerable in that way. The recon advantage is realistic, because carriers conduct basic patrols, notwithstanding their strike and intercept abilities, which would increase visibility.
If my proposition would make carriers too powerful, then perhaps only fighters that haven't used their move (those tasked to intercept, heal, or skip turn) could affect the first strikes and visibility, and not fighters that actually attacked.
One final idea is to have a medium bomber unit, which would be able to be placed on carriers or shore, that would give carriers a bit more punch against shore defenses.
*Whew* that's incredibly long... sorry about that