I own Arsenal of Democracy. When I first tried it some years ago I found it unbalanced (playing as Japan). Shelved it, eventually installed C.O.R.E. and now recently actually played it and really enjoyed it, as in: I was surprised at how good it is. In particular, I found that the way combats work in AoD with C.O.R.E. (though no idea how it works without C.O.R.E.) strikes me as much more satisfying than the dynamics I'm familiar with in other PI games that use the Clausewitz Engine (e.g., EU and Crusader Kings).
My questions are probably beyond what you guys should or could address in this thread, but maybe I can either prompt you to create "History and Ancestral Tree of HOI games" or to point to some existing threads on your forums that would address my questions.
1. What is the "history" of the Hearts of Iron games?
2. How many HOI games are there?
3. How do each of these games compare?
4. What was the reason for the production of each variation/sequel in the family?
5. What were the design/commercial/philosophical goals of each title in the series?
One thing that really strikes me with AoD+CORE: at least for the one position I've tried so far (Japan 1936) the game does a remarkable job of striking a balance between creating historical frame with historical events of an "inevitable" nature, balanced against freedom for the player to explore/create alternative grand strategic visions. Apart from some of the historical scenarios in the Civ series, I can't think of many games I'm aware of which managed to accomplish this so well.