They're not "similar". One was AAW oriented from the start, the other is a multipurpose design, with the final version having a heavy ASW component (at least the French ones). 

You might be wondering about the FREDA, ie the AAW FREMM. Answer is simple : building more Horizons appeared to expensive. Not sure how much cheaper the FREDA will be (development costs, etc) but that's the rationale. Money. 

The Italians will buy American AAW SAMs and systems and use their own good ASW in their own builds.

Politics.

ASTER is a perfectly working SAM system, at least equivalent to anything available in the US oriented ships.

it's modular, long or medium range and you can fit what you need, being it ASTER 30 or ASTER 15, or add new cells if the ship is build to accept them.

Would italy not trust PAAM it would create it's own SAM system: it had done so in the past with MBDA Spada systems and its perfectly able to do that again if needed to, but [url=http://en.wikipedia.org/wiki/MBDA]ASTER[/url] is an Italian creation as much as French, and British and it makes little sense dropping it and start buying under licence from you main competitor on the market.

 

As for the difference between Horizon and FREMM, it's up to what you need to do: British (type 45) have need for stand alone ships, able to create an AAW umbrella for other less capable ships in small fleets around the globe (Falkland comes to mind) and at the moment is lacking bigger and more expensive ship to act as fleet command. RN fleets are small but more numerous and disperse around the globe then France or Italy, meaning buying more expensive type 45 makes sense provide you can afford them.

French and Italy have different requirements: their Horizon destroyers are intended to mainly act as escort for bigger carriers and this is the main reason for the PAAM system and EMPAR integration: For the Marina Militare i.e. , Cavour, Horizon and FREMM all share the same AAW radar and control system meaning Horizon or Cavour can direct the whole FREMM escort missile system in the fleet if necessary as it's own extension. This is the reason for Italian preference for multi purpose FREMM to more specialized AAW: MBDA Sylver 70 is Scalp compatibile, as well as ASTER 30 and 70 giving the fleet a diversified offensive capability not present in larger vessels. OtoBreda 127/64 Vulcano (also used for the upcoming F-125 german frigades) and the MBDA Teseo Mk2 Block IV offer long range costal targeting capabilities in addiction to anti ship and anti aircraft capabilities (for the cannon only).

What a larger destroyer gives you compared to less expensive frigade is superior Fleet command facilities, but you just need one for each fleet. What you get mixing Horizon and Fremm is a force multiplier with the ability to share the same AAW system on board without too much duplication for unneded facilities while adding better ASW and Anti ship capabilities then you'd get on the Horizon or Type 45 .

French Navy prefers many specialized versions, while Italy sticks with "deal with what is coming at you with what you get at hand". IMO through, French FREDA are not as capable as Italian General puropose FREMM which (always IMO) are better balanced ships.

 

In the end what makes a ship SUPERIOR is how well it blends with the roles you intend to cover with it: type 45 may have a slight advantage in the radar compared with EMPAR on paper, but does not has the same level of fleet integration meaning each ship is more of a lone wolf: this may suits RN necessities but would be quite useless if not counter productive for French and Italian navies.