It's largely neoclassical, but with Baroque elements, including the broken arched pediments not often seen by the public as they're located inside the complex, as well as on the exterior walls of the sides of the building down the long passages.
It is under the right-hand one of these that the Taoiseach's car pulls up as far as I know.
The screened facade part is quite Baroque in nature in that it is perhaps excessively/exaggeratedly decorated, and powerful in design; Power's figures atop generating a particularly Baroque skyline.
It's interesting how this building doesn't seem to have won the affections of most people - perhaps an indication of the Baroque influences in its architecture, not to mention the early emergence of modern elements such as the clean chunky lines of the parapet that almost look like cast concrete.
I've never been a fan of the elevated pediment on the central block of the building:
...but otherwise I like the scheme overall. The view through the screen wall with railings in front is very striking - no doubt a lot of pain and effort went into designing that so the screen element and the central block inside hung well together from that important street perspective.
You probably know that much of the street elevation is derived from the Custom House, notably the twin column formations with windows in the centre, and the heavy dentiled cornice - not to mention the Tuscan order employed obviously