The training is mostly identical, clearly with the RAF you'll have a broader range of airframe types to aim for and that may be a better thing in terms of numbers they'll take and success at grading etc.
Operationally you can be specialist aircrew in the RAF and restrict yourself to flying only - this will limit promotion and your salary moves to a specific pay spine. Otherwise you could find yourself being sent into broader non-flying tours (my last three bosses in JFC were RAF aircrew), the more broadening you get the better placed you are to promote and move up within the organisation, if that's your bag.
RN Officers (P & O) can't specialise as such, they are Warfare first and foremost, some may have extended flying careers but given the small number of squadrons that's increasingly harder, some opt quite early to go down the PWO route and aim for either surface command or to dip in/out of broadening warfare and general appointments. When they do the latter its harder to get back to flight appointments.
Clearly the major difference is the operating environment and there is nothing in the aviation world that is as fun, exciting and challenging as operating from a ship in all weather. A fixed airfield is mundane by comparison and will not stretch your training and abilities by anywhere near as much as a pitching lump of metal in the middle of the Atlantic at night, with nowhere else to go.
There are, of course, the disadvantages of being away from home for long periods but counter that with the advantages of being away from home for long periods. You've just got to find the right partner when you go down that road.
Once you're airborne then, for fixed wing, the jobs are very similar and you get to experience all that the Crabs get to do but then you have the fun of going back to your floating airfield. There's plenty of scope to tear around with your hair on fire but probably even more so as there are fewer rules over the oggin.
One of the biggest differences are those of your responsibilities as an officer. The Crabs tend to leave most of their dealings with their airmen/women to the engineering officers on the squadron, whereas the RN has the divisional system. I can't count the number of times I moaned about writing divisional report etc but an RN officer is miles ahead of his RAF counterpart in dealing with the men and women of a squadron. Of course, Jack is more full of banter than a bantering bag on banter day and I know I'm going to get flamed when I say an FAA pilot is so much more in touch with the people on a squadron than a Crab but it is true. I believe this makes both for a better officer and a better organisation. On an RAF squadron, as a junior officer, you'll hold the heady position of being in charge of the coffee boat or maybe organising squadron participation in the village fair. As a junior officer in the FAA you may well be in charge of the coffee boat but will also, and more importantly, have the responsibility for 10-15 ratings' careers and livelihoods and you'd better get that right.
You will never go on a run ashore with the Crabs that would equal an RN night........especially when you decide it's a good idea to make it a divisional run ashore. Be afraid of Jack and his singular aim to get photos of his DO in the most compromising of positions. I'm still being reminded of one of mine in Gibraltar to this day
And, finally, there's the uniform. Why on earth would you ever consider being found dead in the RAC clothing worn by the Junior Service when you can wear navy blue?
Working on the Joint Force Harrier circuit there was a noticeable difference between RN and RAF aircrew, as @Pontius mentioned I think its down to the divisional system that the RAF don't use in the same way. I was the Line SNCO on 1(F) squadron and the banter between both blend of pilot was flowing most days however there appears to be a more "us and them" feel with the RAF and a "we are all in this together" feel with the RN. There was a good number of RAF pilots who I still banter with on FB, however there was a few I wouldn't p*ss on if they were on fire, the same could be said for a few Sea Harrier Pilots (the one that started the engine while I was still on the ladder sorting his crypto!!!).
In a nutshell, join the crabs and fight and dress like a RAC patrol man or join the RN and have your aircraft called an RAF jet/Helicopter every time it appears in the Daily Mail.