Is renting a car better than public transportation in Ireland?

It's hard to know if you missed out on anything since you didn't say where you went. You need to be more specific.

For one thing, a car can get you to out-of-the-way B&Bs in secluded locations that a bus doesn't go near. We stayed in a B&B out in the country near New Ross, where the owner was a driller of artesian wells by trade. He told the kids all about his divining rods and allowed them to try them to find the spring in their yard. They let us fill all of our available bottles with the best water we had the whole trip.

And with a car you can set your own schedule and do what you want to do when you want to do it, rather than waiting for the next bus. I'm sure that buses don't go to places like Monasterboice, far from anything, where we found many perfectly preserved high crosses. If you're on a bus you can't stop and investigate something you see along the way - you go directly from one place to another without stops, except for the ones on the schedule. That, to me, is a deal breaker for taking the bus. I don't find driving in Ireland a "white knuckle" experience at all, though it is different. I enjoy the freedom the car gives me.

I am not a huge fan of renting a car in Europe, but in Ireland it is a must. Part of the fun of Ireland is discovering backroads (single lane often) that lead to places public transportation for which public transport could never get.