And I'd also like to point out that warrior-mages have been around even in 3.0, even before prestige classes like Eldritch Knights or Spellswords. They're called Clerics and Druids.
... with the divine spell list, not the arcane spell list
... the cleric was largely understood to be one of the most powerful classes in 3E
The reality if the EK hybrid is neither of the options you provide. One of the optimal ways to use them is as a wizard who augments their somewhat small pool of available spells by doing some pretty very nice ranged weapon damage (they aren't that far behind an equal level ranger here). Otherwise you just end up with a character that is Jack of All Trades and Near Master of Many (as opposed to the proverbial "master of none"). Out of spells? Get out that two handed sword or bow. Fighter goes down, is paralyzed/held/etc. and no one can fix him immediately? You're far better off filling that role off than you were before. In fact, if you use some defensive spells you are going to be a quite decent tank all by yourself.
...
In fact, one level of spell progression isn't that much. For example, the EK combo you mention, even with a slightly staggered progression, is still casting the same levels of spells that, say, a sorceror of the same level is casting (and while Sorceror's are no Wizard's, they are still plenty powerful and probably better balanced with the other base classes).