These are just a few of the things I notice that Eldritch Horror does better. I still like Arkham, don't get me wrong, but there are certain areas where Eldritch shines, and I think it might be worth house-ruling or modifying Arkham to be more like it in some respects. Some of the big ones:
Bank Loans
The great thing about bank loans in Eldritch is that they are both easy to take, and have interesting consequences. if you want to take the loan in Arkham, you have to trundle all the way to the bank and then all the way back to wherever you actually wanted to spend the money. With monsters to kill and gates to close, I don't have time for paperwork at Miskatonic Credit Union.The consequences of failing an Arkham bank loan also aren't really all that interesting. Bank loans in Eldritch are easy to take, and Debt provides a host of interesting consequences. You can even find yourself embroiled in a Dark Pact due to Debt, which seems much more thematic than just having your stuff repo'ed.It's also a lot harder to weasel out of in the meta-game, which I like. It's just very well done. Really, the best part is that Eldritch really encourages you to engage with the bank loan mechanic, while Arkham seems to punish you more for it, and it's always better to have a mechanic you want to engage in.
Combat
I think I really prefer Eldritch combat. It's just as fast as Arkham combat, but it actually allows for teamwork, which is a good thing in a co-op game, it allows weaker characters to be some use since they can at least contribute to defeating the monster, and it doesn't become a death cycle for characters who get attacked by a monster they aren't prepared for. It's also nice that successes mean something even if I don't roll enough.
Difficulty
First, almost all rolls in Eldritch are made unmodified. In Arkham, almost every roll is -2. -2, -2, -1, -2...it gives a false impression of character abilities, and it is very frustrating. For several characters you might set a slider at 2/2 thinking it's an okay balance, when really you've just screwed yourself out of being able to roll either stat. It's an annoying newbie trap that favors pushing sliders to extremes rather than trying to carefully balance stats. For the most part your skill is how many dice you have to roll in Eldritch.
Secondly, Eldritch always gives you a die. A good number of encounters in Arkham will result in you just not being able to pass them without clue tokens, and frequently you just don't have clue tokens. Nothing is more frustrating than having an encounter card come up at random that you know you have no chance at even passing because you didn't manage to guess the right skill or have extra clue tokens.
Encounters
The real heart of it as far as I'm concerned is that Eldritch encourages encounters, Arkham doesn't. That's it. Encounters in Eldritch are normally positive, and you don't need to lose out on doing important things like acquiring items or healing to do so. Encounters in Arkham tend to be risky and unrewarding. Strategically you want to get through Arkham with as few encounters as possible, and this is a shame because that is where the narrative meat lies. Eldritch is really good about not just making encounters worthwhile, but forcing you into them. I'm convinced one of the reasons my group initially struggled with Eldritch is because we had become conditioned by Arkham to run screaming from encounters, so that we lost out on several opportunities later on in the game.
No Sliders
While I don't mind skill sliders mechanically, physically I find them troublesome as they keep sticking to my hand and getting knocked off or blown off the table. For all those crafty people making monster holders or gate holders or card trays or whatever, some custom sliders with more weight to them would be the biggest boon at my table.
Rarity of Items
I have to say I really like how unique items (artifacts) are, well, actually unique in Eldritch. Getting an Artifact requires an Expedition or occasionally a lucky Other World encounter. You don't just pop down to the local Magic Item Shop and pick up what you need. It makes them feel special and for OP as they are the fact you need to go out of the way to get them makes them feel special and rare, as opposed to something every character at the table will have.
Spells
Most spells are just better than there Arkham counterparts. I also like that most spells get some kind of additional effect for more successes on the Lore check, as opposed to Arkham where there is almost never any difference between getting one success and getting three+. Spells in Eldritch feel really useful despite being dangerous, where spells in Arkham tend to feel like a last resort when you don't have anything better. Arkham does have some good spells, but the bulk are frankly terrible.