being a resident can determine if you have a credit score or not and your credit score matters when getting a loan.

If you have low credit or no credit you'll probably need to make a bigger down payment than if you have a 700+ credit score.

At that stage you would qualify and receive the same interest rate. Lenders don't set rates based on citizenship.

@John:
I'm on H1-B/AOS (final stage of permanent residency).
If I do get a loan, will the interest rate be higher just because I don't have the "green card" yet ?

Yes, they do. Lenders for the most part will look at citizent and permanent resident aliens as the same, while variations in Visa types will determine the ability to qualify for a home loan. Temporary visas for education rarely will work while H1-B visas will normally suffice. Do you have a specific visa type you are looking at?