Tennessee’s pop density seems to be a little lower than Ireland’s. Now, Ireland is not known for its good public transport, but just Dublin’s commuter lines have something like 100x the peak capacity of the Dollywood train.
And Ireland’s anemic rail network is more a result of no investment from the 50s til the 90s than a density thing, really; there is clearly demand for far more capacity and they currently can’t build it fast enough.
The DART (Dublin's commuter rail to and from its suburbs) is great (as are the Luas trams around the city). The inter-city trains going to Limerick, Cork etc. (which many Irish I've met don't even know still run) remind me of Amtrak and not in a good way.
The Limerick one is very, very bad, granted. The Galway one is actually now slightly slower than the bus! (Though still far more pleasant than the bus.)
AIUI nearly all rail travel volume is on the Dublin and Cork commuter lines these days; the intercity ones are kinda an afterthought (the only one to even manage hourly operation is Dublin to Cork at this point, I think).
And Ireland’s anemic rail network is more a result of no investment from the 50s til the 90s than a density thing, really; there is clearly demand for far more capacity and they currently can’t build it fast enough.