Cause EK probably can't do half melee damage an SS can - particularly when spending AP.
Also EK can't easily tank early on and has worse progression.
An SS always has great AC and the right tools for the job - sufficient weapon enchantment to surpass any DR, Spellstrike to effectively damage enemies with DR that cannot be beaten - like elementals, Ghost touch VS ghosts, Brilliant Energy vs high armor (though its least useful).
What makes you say EK cant do as much damage as a SS? Don't have much experience with SS, but from what I've seen they shouldn't be to much better than what the EK can do.
EK ends up with 4 attacks and 16 BAB if built right (higher than SS I believe? Or does SS have full BAB progression?), level 7-9 spells which is a big deal in and of itself, access to spells Magus can't normally get, namely sense vitals amongst others (unless you use spell blending with the EA mod I suppose, still can only go up to level 6 though), can actually make use of arcane strike feat, etc.
My EK build also has decent AC, maybe not as good as a sword saint, but pretty good nonetheless thanks to a monk dip and protectors robes and with all the usual arcane defensive spells is pretty tanky.
I'm curious as to what you think of the EK class as a whole.
EK class is cool for people who want to focus on casting, with melee as support. SS the opposite. Also a Sword Saint has a much nicer start and better progression. An EK doesn't get much apart from spells till level 15-16 (provided that he does not multiclass further).
Why more damage?
1. Lethal Focus to add Int mod to damage: +9 damage, multiplied on crits (vs flat footed, but with my playstyle all enemies who can be feared are perma flat-footed)
2. Bane Blade for +2d6 damage
3. Alignment based damage: +2d6/+4d6
4. Elemental damage, depending on how much you use alignment bonuses (how much budget is left), generally +1d6 to +3d6.
5. Greater Weapon Specialization for another +2 damage, if you feel like it.
6. Then you have Critical Focus to make sure your crit threats actually land (Int mod added to Crit Confirmation).
Of course if you use Craft Items to create even more OP weapons then the game offers, this gap is less. But I don't think it can be fully closed.
These are practically permanent bonuses over EK. You Enchant weapons before combat (end game it lasts 19 minutes and can be reapplied multiple times when needed) and still use Arcane Strike normally, unless you NEED special Accuracy boosts (like Arcane Accuracy adding Int to AB). Perfect Strike does not comsume Swift Actions.
Number of attacks is usually the same - with Spellstrike you get the "free" attack with Spell Combat one-handed, but I like Transformation with 20 BAB two-handed even more.
Then when you need to nova, you trigger Perfect Strike and/or Perfect Critical (in fact I use Perfect Critical most of the time and mosty enable Perfect Strike for singular Greater Vital Strike Attacks) and maximize weapon damage plus increase the crit multiplier for at least 30% more damage - way more with the like of GVS.
Then you get nice bonuses:
1. Int added to Initiative. Eventually you always roll 20 on Initiative rolls.
2. Int added to number of attacks of Opportunity.
3. Obviously Int added to AC
4. Easily able to pierce Silver, Cold Iron, Adamantine DRs when they first appear in game. Casually butchers ghosts. Spellstrike efficiently solves early Elemental issues. Brilliant Energy destroys enemy AC in Chapters 4 and 5.