I did my (RIBA) part 3, 14 years years ago in the UK. At that time the procedure was that you had to have a minimum of 2 years post grad experience, have a satisfactory log of that work, carry out a 'thesis' or building study on a project in which you had been involved and which had been completed on site, your architectural thesis (if you were from Bolton St) had to be accepted and approved by their external examiners, you sat a series of written exams and then completed an oral examination. For reasons which I can't exactly recall I was exempted the written exam (something to do with the fact that I was already a registered Architect under ARCUK). but the Oral Exam was then beefed up to a full examination and everything 'hung' on that.
The main difference with RIAI part threes was the range of contracts (about 14 then) which you had to be familiar with under the RIBA set up - as opposed to the two or three forms then in use by RIAI.
I did the RIBA exams purely because I had been working in London, never worked in Ireland and had no familiarity at that stage with the system here.
That said if anything I think the RIBA system is slightly more rational and structured - I've always had a vague suspicion that the institute here operates a Quota for passing part 3 students - no evidence of that with RIBA.
RIBA is recognised here for all practical purposes and yes you can join RIAI once you have RIBA without anything more strenuous than an interview.
That said I never bothered applying and am still RIBA rather than RIAI.
Hope thats some help