Essentially, EF = designed for agility and air superiority (although called 'multi role' it does seem to be more of a dogfighter - to me anyway) and F-35 = stealthy deep strike aircraft. (Ok, thats kinda dumbed down and doesn't really cover all the bases but you get the point) these aircraft COULD do eachothers job just not very well (and even mentioning putting EF on a carrier is pretty silly).
Look up the F-35 thread and look up about it, comparing it to the EF or Rafale is ridiculous, its streaks ahead anything the French have (or planning to have).
The AA varient of the FREMM - FREDA - will be built in very small numbers (looking at Wiki, the French are having 2 and the Italians aren't having any), and they carry less Asters, 16 less to be precise.
FREMM is a multi-role frigate platform and as such will be slightly handicapped against a role-specific destroyer such as the T45 even in an air-defence configuration and i expect its radar will not be as capable as SAMPSON so for air defence, the T45 would be more effective.
A better comparison to the FREMM would be the coming T26 frigate as comparing a dedicated AA ship against a multi-role system isn't particularly fair and the system which you described as 'less capable' i assume is CAMM? Which isn't coming in as a 'downgrade' of Aster but an 'upgrade' of the SeaWolf missiles aboard the T23 (and later T26) although I do appreciate there will be no AA T26.
(Old FREMM thread but give it a read through
http://www.defencetalk.com/forums/navy-maritime/new-details-fremm-aaw-variant-6691-7/ )
Ultimately, we do put in a large amount of money and come out with generally few ships to show for it, but what we do come out with is pretty good.