Older model and the new G2 are both DAO. Newer model has less checkering, 3 dot sights, rail. In the specs in the catalog, the pistol is listed as 10+1 but elsewhere 12+1 like the older model. The Glock trigger is a new feature and the take down mechanism is actuated by a pulldown gizmo rather than a twist/pull-out pin. Looks like the pistols are pretty much the same otherwise and I think there isn't enough improvement or evolution to make me give up my old PT111 which is a gen 3 (12+1 with Heinie sights).
OOOPS the above is my description of the difference between the new G2 (not to be confused with Gen 2 and the Gen 3 I own)... the Gen 2 held 10+1 and the checking was different. The Gen 3 has a DAO trigger as I noted. In order to have the single/double action trigger you mentioned, the pistol would pretty much have to have some sort of hammer and none of the PT111 family does.