I agree re private schooling, I went to private schools all my life and and the teachers are no better if not worse that those in state schools. I intend to send my kids to state schools, you are better off saving your money for college fees.
It depends where on Dublins south side you are thinking of moving to.
Areas vary wildly as do schools.
I think one's estimation of how good a school is also depends on how you grade or rank schools and what you consider important for your children's development - is your criteria how well they do in exams and in particular the Leaving Cert or do you feel that a non denominational education is more important or is access to sports and other facilities a primary concern, or is the state of the school buildings themselves important? I think you need to think about some of these things when making a decision.
You may already be aware but just to let you know that state schools are primarily Catholic ie they teach Roman Catholicism as an integral part of the curriculum. There are a number of schools run to the Church of Ireland ethos and they normally give preference of attendance to those who are members of the Church of Ireland (at least they do in my area anyway). There are other non denominational schools ie Educate Together but they are not universally available.
As for which is better - state or fee paying, there is no one answer - it all depends; as Draoighonta said it depends on the location but it also depends on the child as some children end up doing better in one school versus another.
As an example - I live in Greystones and the opinion that I have formed is that the state Primary level education ie age 5 to 12 is excellent in the area and there is no need to send my kids to private school. However, currently, I feel that the secondary level (ie age 12 to 18) state school in the area is not as good as others that may be available so at the moment I am planning to send my kids to private secondary school. I based my decision on conversations with parents and past pupils of the local state school, published college entrance results and the physical state of the building and the extra curricular activities offered. Other people may undertake the same analysis and come to the conclusion that the state school is perfect for their children.
The other issue is if you decide to go private schooling then, in many places, you are into waiting lists and uncertainty over whether your children will get a place in the school you want because of excess demand - it would be worth making a few phone calls to see what the availability of places is if you decide on a school you like.
Anyway - they're my thoughts and aplogies for the long post