The reason there are two programmes is that the requirements are different - and history has shown that trying to make one type fit both land-based and carrier-based is rarely successful. F111B is the poster-boy for that.
What that tends to suggest is that the airframes have to be different in both strength, low-speed response, approach characteristics etc and then you're into material resistance to seawater corrosion, sealants, EMI/EMC when in proximity to high-power emitters.
That doesn't stop you using common components in the design - engines (if materially compatible), radars, comms etc (see EMI/EMC), seats and so-forth. It's probably where you might find the most savings logistically, but the devil will be in the detail. Which is probably why most primes spent quite a bit of time re-inventing the wheel so to speak, because its sometimes quite difficult to prove that component X (acquired for an AF programme) meets all the requirements for operating off ships.
Not entirely sure in this case that the performance / role requirements are that different. The USN could really do with leggier jets than the SuperBug.