All I know is that every build I make even remotely able to enter it go out and grab Eldritch Knight 1. Just the first thing to occur to me.
Eldritch Knight is a surprisingly bad choice for a Mage that wants to go gish. It is, in fact, probably the worst choice. First level loses you a caster level and, in return, grants you a bonus feat... from the Fighter list. In effect, it is no different from taking Fighter 1, except for the slightly different skill list. Functionally, it is the same.
By comparison, Abjurant champion can be entered *without* taking levels in a class that grants full martial proficiency (just one will do), full BAB, a bonus to your already strong Will save, extended abjuration, which is basically Automatic Extend Spell for all abjuration spells, which is just plain awesome since it frees up lots of higher level slots, and it gives you Abjurant Armor, which is a free +1 to AC for any abjuration that increases it, just for the heck of it. *AND* you don't lose a caster level for any of it. The drawback is +5 BAB requirement, which means as single-class Wizard, it's not possible to qualify before level 10.
But there are many and more Full Bab/Full or Near Full casting PRC's out there for Arcane mages. Of them all, Eldritch Knight is probably the loser.