Better than what?
I have no idea what the situation is in Ireland but if it isn't good then they are very much an outlier in the EU community!
I live in Luxembourg; I have an electronic vaccination card (and a paper one) and I and I am prompted by email to make an appointment with the appropriate service provider every time a vaccination is due.
Chicken pox vaccine is widely used here as is it's adult equivalent, the vaccine against shingles (of which I am due a dose in a couple of weeks).
All of this, I hasten to add is completely free - unlike most medical services in the USA