Which one is harder to attain, a nomination or an appointment?
Yes.
The question is a bit loaded, and even if you had a clear answer, I don't think it would be worth much because you still have to get both.
While it is certainly true that (in almost all cases) a nomination is required before an appointment is given, the matter of which is "harder" to attain is dependent on too many factors that change too often to permit a clear answer. When getting a nomination (and depending upon the source of the nomination) the competition you are up against will be very different than that faced for an appointment.
How many applicants? How strong are they? How many slots does the nomination source have available to them for YOUR desired Academy? How many of those applicants are second-time applicants? How many are NAPSters? What state are you in? Etc., etc. All those factors come into play when a nomination is sought. As for the appointment, it's the same questions, but on a larger scale.
So the ultimate answer to your question is, IMO, "Who cares? You have to get both anyway!"
Now, one thing I CAN say (and from personal experience) is that getting the appointment is EASY. It's GRADUATING that's a cast-iron *****!
But hey, nothing worth doing is ever easy, right?