My personal preference would be to use a low cost flight service to Ireland, and pick up a rental car. That would allow me to travel each day at my pace, itinerary and timetable, rather than one which suits a coach tour operator. The Irish Tourist Board can provide loads of useful information and itineraries for those on a self-drive holiday.
The disadvantage is that as the driver, having to keep my eyes firmly on the road ahead would mean that I may miss some of the spectacular scenery, as well as the informative commentary supplied by a tour guide. But I could stop as little or as often as I like, spend as much time as I wanted in each place of interest, and eat in places and at times which suit me.
On a coach tour, I could perhaps relax more and from the elevated seating position, could perhaps see more than I would in a car. But to take full advantage of the daily excursion programme, it would mean being up very early each morning for the fixed breakfast times. Perhaps not so good if you have been enjoying the hotel entertainment until 3am that morning !! Stops on the itinerary will include places which pay the driver and tour guide generous commission, such as Irish pottery or crystal retail outlets. These are often remote from towns, so after a couple of days when I get fed up being part of a captive audience at these shops, the only alternative may be to sit on the bus and ponder how long it is until the next scheduled stop or fixed meal time.
Self-drive is not an option for everyone. Even licenced drivers may not be too keen on spending a week driving around unfamiliar roads. But even if I was not in a position to drive myself, I would still fly to Ireland and use public transport to travel between some of the main towns and cities. I would stay in some of the excellent hotels or B&Bs, and perhaps just take the occasional local coach trip to explore the Irish countryside.
I suppose in the end it all comes down to personal preferences. Do you like to have your full week's holiday planned in advance for you, be told where and when you will be going each day then sit back, relax and hope that you will get on with your new travelling companions ? Or would you prefer the freedom and flexibility of planning your own holiday programme, which you can then adapt as and when required during the course of the holiday ?
David