I think competitive is a fair statement. For the areas surrounding Raleigh/Durham, you can expect a written exam, a scenario, an agility exam, and some type of interview. I would imagine MEDIC is similar. check the websites of the individual agencies, most list their hiring procedures.
Not everyone who applies get hired. I've seen academies where as small as 3, and one as large as 50. Most places that run academies are only hiring full time employees; I know of one place that mandates even part time hires complete the entire academy. Not every agency runs an academy, but more are doing it to acclimate you to how they want things done. Personally, I think running an academy for full time new hires is a great step in standardizing how thing are done.
From what I have been told, the academies serve two reasons: 1) to ensure all new hires are told the same information, and to allow for some consistency on departmental protocols and 2) to see how well a new hire can adapt to the way an agency operates in a classroom setting. They don't want to fail anyone, however it's better to remove a new hire in the academy vs in the FTO rotation. Some academies are harder than others. In every academy, people end up quitting (it's not for them), or they get dismissed for various reasons. But the goal is to get you to complete the academy successfully.
I would imagine (and this is only a guess) that 75% of people who start the academy will graduate. As for who is still employed, well, that depends on the agency and the individual. But it's definitely not an impossible task, if that is what you are worried about.
If I can be of any more help, feel free to PM me.
Moodie