The crux of it is this:
The Arcane Archer can make magical arrow attacks twice per short rest, or slightly more often at 15th level. The Eldritch Knight can make magical arrow attacks pretty much all day long starting as early as 7th level. So if you want to shoot magical arrows instead of regular arrows (half damage against demons, no damage against werewolves, etc.), you pretty much want to be an Eldritch Knight, not an Arcane Archer.
There are some ancillary issues too like the Eldritch Knight getting to summon his bow magically and having some other archery-relevant spells available to him, but the core of it is really that. If Arcane Archers just got to count all of their ranged attacks as magical it would go a looong way toward providing them with an actual niche, despite the relative lameness of their actual Arcane Shot options.