(International) MIT vs Stanford -- Which for EA?

I don’t know whether I should apply to MIT or Stanford early as an international student.
I really, really, really want to go to Stanford, but since they’re need-aware for international students applying for aid I don’t know if that’s the best choice.
I don’t mind MIT (better stated, I’m not particularly fond of them) but I think I have a better chance of acceptance if I apply there early.
I know that for EA it’s best to go with your gut/heart/whatever internal organ, but I just don’t want to waste my time applying.
What should I do?

Go with your entrails! Seriously, applying to Stanford or MIT EA does not improve your chances of admission, and neither option is binding anyway, so you lose nothing by applying EA to one and RD to the other.

Apply to Stanford. That is where you want to go.
Don’t apply to places you are not fond of. You have to go there for 4 years.

Don’t agonize over applying to either; your chances of admission are statistically pretty low at both schools.

Are you considering applying early anywhere else? You could apply EA to MIT as well as EA to Caltech, Chicago, etc.

If you apply SCEA to Stanford, that is the only private university to which you can apply early.

Your odds are 1-2% at both. So, apply to Stanford as you would play the lottery, then focus on universities with merit scholarships where you have a shot.