The two games are rather different in their game mechanics. Heroes of Neverwinter is a more tactical game which isn't unlike actual 4th edition D&D. Arena of War has a far stranger combat system, where you slingshot your hero against the monsters and damage is determined by how many times they bump around and into what obstacles. Part pinball, part Squids (another iOS RPG). But what the two D&D games have in common is that you don't play only your character(s). Instead you play your character and party members which are controlled by you, but are "borrowed" characters from other players.
And that really doesn't work very well for me: You can group with borrowed higher level characters, and your own character will barely have a contribution to the success of the adventure. In Arena of War you even just get random characters to play with you, which sometimes are much, much stronger than yours. But of course you can only level up your own character. Not much fun if leveling him up doesn't matter at all in view of his much stronger companions. There doesn't even appear to be any better reward if you do adventures with lower level companions.
Arena of War is further marred by an energy system where you run out of quest energy very quickly, and it takes hours or money to get it back. So while I do actually like the weird pinball combat system, I consider Arena of War nearly unplayable because of the social system and energy system. Hasbro really should take better care to whom they sell those D&D licenses.