We are about to renew DS1's passport and get first one for DS2. Because DH and I have Irish passports we are applying for Irish ones. I don't know that it will be easier but I think it's part of my process that says they will choose who they want to be when they want to. I can't call my boys English or Irish. They are Londoners and so having to change their passport or not might be a tangible way of, in the future, allowing them to identify who they are in terms of nationality. They will always have a heritage from their parents in that, at the very least, they will probably be very good at mocking a Northern Irish and a southern Irish accent
I have UK-DH has Irish -makes no difference at all which you have. We have lived abroad etc., gotten visas for lots of countries and always the same for us both. Only issue is it's easier to renew whichever passport you have if you live in that country! Having said that both are fairly straightforward. Follow your heart!
I think it might be easier to get into the US with an Irish passport, though that may be an urban myth! I also seem to recall there is a small loophole whereby Irish citizens pay EU fees at Scottish universities - without needing to fulfill the normal 3 year domiciled criteria.
It depends where you want to live. The UK permits dual citizenship so you may be able to have both, but I don't know if Ireland permits it.
There are certain advantages to obtaining British Citizenship if you intend to live in Ireland, and vice versa- but these relate mostly to situations where you have family members who are non-EU nationals.
The UK is better in terms of health and social care provision, but again that depends where you want to live. You may also find that it is easier to travel abroad with a UK passport.