Really late reply, but finally played it last month.
AH3 is pretty much another version of EH, which was something of a revision of AH1&2 (iirc, The only differences between AH1 and AH2 was the gameboard -- EH is not AH2), which were nearly identical. So if you like your copy of AH1or2 or EH, then there's no need to buy AH3. I figure I'll pick up AH3 if it goes at a deep discount, or I want more Lovecraftian gaming content. (The last two big box expansions for EH were underwhelming for the price, according to various BGG'ers.) If you don't like the sf-looking modular boards, then you'll still find them detracting in the game. If you've played the CoC LCG, then you'll recognize the draw bag mechanic, which replaces the Mythos cards. While you're still drawing a card for an encounter, Gates have thematically changed. Rather than going to another dimension (which didn't happen all that often in Lovecraft's stories, and pretty much never to a dimension that was not thematically related to the Ancient One in the story), doom tokens are added to a sector -- er, neighborhood -- and you draw from a different deck, representing the influence of the mythos. It's more story-like and subtly shuts down neighborhoods, since you aren't drawing from the (sometimes) beneficial neighborhood deck anymore. Also, research tokens have thematic rules that (iirc) differ with each scenario, rather than act as bland flavorless tokens. If I didn't already have AH or EH, I would start with EH3.
MoM is a very different game. The difference between AH/EH and MoM is sort of like the difference between Talisman and Descent. In AH/EH and Talisman, each player runs off in their own town or world location and does their own thing. With MoM and Descent, players work together in the same room (or at least close to each other) of a house. With MoM2, an app controls the game, much like a game master.
AH2:
https://boardgamegeek.com/thread/2042520/how-we-play-arkham-horror-2nd-edition
