I've played both Arkham Horror and Eldritch Horror pretty extensively, and I have to say that hands-down of the two I greatly prefer EH. While it's difficult to say it's less complex than Arkham (because it really isn't), it feels like you get a lot more bang for your buck out of the complexity. Arkham, for all of its systems, almost always comes down to Gate Token Whack-a-Mole, gameplay-wise, and everything else just feels like a distraction from that. (I haven't played it, but I've heard similar things about the Android board game, from the same designers) Eldritch Horror feels more like there's a story involved, like you're advancing a narrative as you play. These days, when my roommate says he gets the itch to specifically play Arkham Horror instead of Eldritch (he owns the former, I own the latter), he admits it's entirely out of frustration that once he went on a spending spree picking up the expansions only to find most of them lacking and he just wants to make sure he got his money's worth. (It doesn't help much that for the most part, the Eldritch Horror expansions are just better for the most part. When we've played Arkham Horror with an expansion board, it becomes Just One More Thing you have to go out of your way to keep track of so you don't lose as fast. The Eldritch Horror expansions give you ways to engage some of the side content on your own terms.)
Also, just a suggestion, if I may. There's an optional rule mentioned in either the core set rulebook or (I think) the Mountains of Madness expansion that I find makes it easier to get into a game. It adds one tiny step to setup, but the end result can't be beat. Basically, you know how there are three 'stages' to the Mythos Deck, and Mythos cards come in three difficulties ('easy' ones with glowing runes, normal ones without anything special, and 'hard' ones with tentacles)? Well, there's an optional rule where you populate the first stage entirely with the 'easy' cards, the second stage with the 'normal' cards, and the third stage with the 'hard' cards. The end result is that you have a staggered, occasionally-increasing difficulty. Over the course of an entire game, it doesn't make things easier but it gives you a lot more breathing room at the beginning to make plans and start acquiring what you need to solve Mysteries. But because it gets harder and harder as it goes, with little chance for a reprieve, it potentially puts you on a bit more of a clock in the grand scheme of things.