I've taken both and agree with TC, no way to actually make a call to do one over the other. Both had outdoor experiences, neolithic experiences, a little bit of city stuff, interesting history and sheep dogs.
I would NOT do them back to back, lol. I did the Best of Scotland back to back with Villages of Southern England and even "I" got castled out by the end of the Scotland trip. I could barely drag myself thru Stirling Castle which was excellent but more than I wanted, lol.
For both I would suggest planning to arrive 2 days ahead if you have that amount of extra time. There is a lot to do in Dublin including taking a day trip out to Newgrange and there is a tremendous amount to do in Edinburgh (although now it may start in Glasgow?). I like the changes that have been made to the itinerary of the Scotland tour - would have loved to visit Skye so that is a bit of a plus.
By the way...the Scotland trip is the ONLY tour I've done (11 Rick Steves and 11 Road Scholar programs) where I wished I had had my waterproof rain pants. It was the Oban to Mull to Iona day and it was lashing rain. Even with a waterproof jacket I was soaked. Thank goodness the B&B had very effective towel heaters which radiated enough heat to dry out my shoes.
We managed to hit Ireland in a heat wave/dry spell but I would want a waterproof jacket with hood for this trip as well.
Do you have any ancestral ties to either country? That can be a way to decide which one to do first, lol....