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I have my doubts on this one but I'll try: My Illogical Theory
The Gen 6 starter types have been following a particular order: every starter is very powerful against another one.
This means that each starter has two STAB moves that will hit another one super-effectively. Like Chesnaught's Grass/Fighting combo, both STABs would hit the Water/Dark Greninja super-effectively, and the same applies for the rest.
Getting to the question, while Chesnaught can knock out a Greninja with any item (yes even Focus Sash), Greninja can take out Delphox with any item, Delphox cannot take out a Chesnaught that holds the new item called Assault Vest.

Also the fact that all the other starters have atleast one stat at 122 (Greninja has speed, Chesnaught has defense), Delphox alone does not reach that limit.

Long in short: Delphos has a better BST than the other starters mostly because Gamefreak wanted to equally balance out the starters.

Hope I helped!

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252 SpA Life Orb Greninja Hydro Pump vs. 4 HP / 0 SpD Assault Vest Delphox: 265-315 (90.7 - 107.8%) -- 43.8% chance to OHKO

This calculation proves this answer wrong. The calculations are of a Greninja EV trained with max Special Attack VS a Delphox with only 4 HP EVs and an Assault Vest. Greninja is also holding a Life Orb.

Therefor this answer is incorrect.
252 SpA Life Orb Delphox Fire Blast vs. 252 HP / 0 SpD Assault Vest Chesnaught: 361-429 (95 - 112.8%) -- 68.8% chance to OHKO

This calculation is what made me do this. There's this fact that has been proved that Greninja is the strongest as it carries Extrasensory for Chesnaught, while Chesnaught is in the middle as utility support is very good, plus it gets Bulletproof to cement itself against attackers like Gengar. Delphos however has no such aces,if it ran Assault Vest then you might as well forget about the Magician ability it has.

Therefore, this answer is not incorrect, it's just proving that Gamefreak wanted to balance them out, it was just that they couldn't make major differences, so it can be told as Gamefreak's best attempt to b alance them out - giving it a 4+ BST in a stat (presumably sp.def).
You don't need Extrasensory. Ice Beam gets the job done.
Also note the fact that Greninja can easily run a physical set to counter that, while Delphox cannot.
How does that calculation have anything to do with the one I ran? Delphox can still survive an attack from Greninja, and that's all that matters. You clearly stated "Greninja can take out Delphox with any item" and that is wrong.
But your calculation is not the max damage Greninja deals in rational sense. this is the max damage it can deal:

252 Atk Life Orb Greninja Night Slash vs. 4 HP / 0 Def Delphox: 315-374 (107.8 - 128%) -- guaranteed OHKO

I guess that's that, there's no avoiding certain defeat for Delphox, even Focus Sash just keeps it alive for enough time to be killed by priority. Chesnaught and Greninja, on the other hand, can set-up hazards on that turn as well, which is a boon Delphox missed out on.
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It does have slightly higher stat total, but 4 stat points isn't much and past starter Pokemon don't have same stat totals either, and Delphox is by no means better than Greninja and Chesnaught. Greninja is frail but has a very high speed stat, and provides great coverage and is a threat in OU because of that . Chesnaught is less used because Talonflame destroys it in OU, but it is still a very good defensive Pokemon. Delphox is probably inferior to both of them.
Only Game Freak can tell you the real answer.

Source: Experience

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*BST stands for Base Stat Total
Well, first off, Delphox only has a 4 BST difference, which isn't very much. In previous generations, the starter Pokemon have had a slight difference in BST as well. For example, Swampert has a BST of 535 while the others have 530.

There is no true explanation to this. However, it doesn't make much of a difference at all. My theory would be that the developers thought it wasn't good enough therefor it needed a little boost?

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