Complexity of Eldritch Horror versus Arkham Horror
I own both AH and EH. I have the Kingsport, Innsmouth and Black Goat of the Woods expansions for AH. Only have the base game for EH right now but those four expansions call me pretty loudly. I really couldn't say that either is better than the other because I really love both a lot but for different reasons. 

One thing that I can say I really miss from Arkham when I play Eldritch is how the investigators interact with the monsters. I like that in Arkham the monsters move around, block your path and can straight halt your action when you run into one. Sometimes it seems like those cardboard tiles somehow know what we're trying to do. I'm really not much of a fan of how unimposing the monsters are in EH, I mean, in real life, if you're sitting there and all of a sudden a portal opens up where you're at and spits out a Shoggoth you probably won't be going for groceries, you'd run, hide, fight or die. In Arkham you pretty much have to make one of those choices... 

However, in Arkham when a portal opens where you are you're sucked through instantly before it even spits out a monster, then you're delayed in whatever other world opened up (in AH every gate has the name of an other world that it connects to)then you gotta find your way back to Arkham(you'll have two encounters in the other world before you move back to Arkham), close that gate, which requires you to do a test of either your fight skill or your lore skill plus or minus whatever modifier is on the gate), then you get that gate as a trophy (if you succeed the roll, success is still a 5 or 6). THEN, if that Shoggoth never moved(each mythos phase makes certain monsters of a type specified move, but you never know what will move or where it'll move to) then you can't move past it unless you succeed at an evade check(which is a test of your sneak skill plus or minus the monster's evade mod). If you fail the test the monster deals you its damage and then you have to fight or just not move. 

Arkham's game world is more alive, much more intense and forboding and much more rules heavy in terms of stuff you gotta keep an eye on each turn, but winning gives a real sense of triumph and there's much more player freedom.Arkham rocks, rocks. Great way to spend a weekend with friends.

On the other hand, Eldritch's game world is more streamlined, more static and funnels players along in a much more controlling way, BUT as a result of that it tells a more comprehensive story thsn Arkham does on a game by game basis. 

If Eldritch Horror was a bestselling novel, Arkham Horror would be the five star epic survival horror (and AH very much is, EH can be tough but AH can and will beat you senseless)video game RPG adaptation. Eldritch Horror tells the story but Arkham lets you live it... but on that note you should really think about checkin out Mansions of Madness too. If I could play that game solo I'd own it in a heartbeat (but one of my best friends has it and all the expansions so we just play his). It could also be said that if Arkham Horror was the book then Eldritch Horror would be the (good) movie based on that book.

Also, like EH, you can play solo which I highly recommend doing for playing for your first couple games(unless you have an experienced buddy who can bring you up to speed) so that you and your friends don't have to spend the day reading rulebooks. Plus it's a blast to play even alone (I suggest playing at least two investigators for solo games though, Arkham's a pretty formidable place for a lone ranger). Sorry to go on and on, just love these games. Hope this helped. Have fun! :)