new iphone replacement over refurbished iphone

You can't, and it will probably be a refurbished phone.

No there isn't.

Copied from the written warranty.

http://images.apple.com/legal/warranty/docs/iphone.pdf

+If a hardware defect arises and a valid claim is received within the Warranty Period, at its option and to the extent permitted by law, Apple will either (1) repair the hardware defect at no charge, using new or refurbished replacement parts, (2) exchange the product with a product that is new or which has been manufactured from new or serviceable used parts and is at least functionally equivalent to the original product, or (3) refund the purchase price of the product.+

If you receive a refurbished iPhone, you will not be able to tell any difference. A refurbished iPhone is probably more closely inspected and tested than a new iPhone before leaving the factory, and the original warranty remains in effect.

A refurbished iPhone is basically a new iPhone. They can't refurbish parts like if it were an old floppy disk player. Hence, all the parts replaced in a refurbished iPhone would be new parts anyway. The replacement phones, I've seen them, have spotless cases that look to be totally new. You'll never know the difference. Relax and enjoy your phone.

I exchanged my quirky iPhone and the "new" one was in a plain white box with nothing but "part no. 661-4412" on it.

The packaging screamed "refurb!" but the hardware looks absolutley brand spanking new.