Hi, Gone Fishing. I haven’t played Arkham Horror, yet. I have friends who have enjoyed playing it.
If you want to play as an investigator encountering Lovecraftian monsters and trying to defeat them, then Arkham Horror seems like a good choice.
Cthulhu Wars is more of a battle royale of Lovecraftian horrors after the point where humanity has failed to stop them. The designer is the same guy who created Call of Cthulhu.
I have played Hills Rise Wild, which is sort of a miniatures game on a board. Everyone controls hick cultists trying to get a hold of the Necronomicon. It isn’t very good.
I have just gotten Fate of the Elder Gods, where each player controls a cult and is trying to either be the first to summon their elder god or be the one who has gotten the least interference from investigators. It looks good.
Mythos Tales is in the style of Sherlock Holmes Consulting Detective. You are given a map, a mystery and you travel around trying to piece together the solution, visiting locations and interviewing witnesses. It isn’t a boardgame so much as a mystery story that the players try to solve and you can only complete each scenario once as you then know the solution. It’s a brain bending experience though.
Pulp Alley or Strange Aeons are miniatures games that work well for this type of setting.
Hope you find a Mythos game that will work for you.
Check out the list here, you can sort by rank.