My general experience is limited to PC games, but I offer the following observations.
I am not sure games like Civilization, Victoria, Europa Universalis, and other nation building or global war games are properly AH, even though the player will inevitably "change history" in wildely divergent ways. Also, just about any good historical war game allows you to change history, but just because a player can win the Battle of the Bulge as the Germans in a game does not make the game itself an AH game! For me to consider a game AH, the game needs to be explicitly set in an AH, with a defined backstory, such as the HOI-2 Armageddon add-on, which sets up an entire alternate geopolitical situation in 1936. I'm also not sure the two Modern Warfare FPS games are really AH...arent they set slightly in the future and are not really an altered past history? They are good, though.
I would suggest the following as my favorites:
War Plan Orange. A strategic-operational level PC simulation of a number of hypothetical Pacific War scenarios based on a US-Japanese war in the early 1930's. Very detailed and, given the fact that it is basically an animated board game, surprisngly immersive. Takes forever but you get to play around with lots predreadnoughts of "never-were" ships cancelled by the Washington Treaty.
Crimson Skies. I've only played the PC version, which is set in a well-developed (but highly unrealistic) AH. Fun arcade-style fight simulator with good story and voice acting.
The aforementioned Hearts of Iron-Armageddon add-on. Confederates vs the Russian Empire vs a Communist Britain and other implausible silliness. Fun histories of the fictional 1936 powers are provided.
Il-2 Sturmovik 1946. The last official version of the very best WW2 combat fight simulator ever came with an AH scenario and player campaigns based on a PoD that the Normandy invasion failed, there was a short lived anti-Nazi coup in 1945, a short armistice, and then resumption of war between the USSR and Germany in 1946. The whole purpose was to let players fly around in lots of late War German "X-planes" and early Soviet jets. For what is really just a detailed survey flight sim, the AH was surprisingly well-thought out. One version or another of this game has been on my HD since 2003 and its still my favorite way of wasting time. With numerous mods now available it's still new.