why is the Note 2 still more expensive than the new S4 at Verizon?

The Note 2 still has to date the best (see: highest objective quality) screen of all AMOLED devices on the market. This includes the S4. RGB AMOLED displays are expensive to manufacture, I wouldn't doubt for a minute this is part of why the Note 2 is so expensive.
 
Best Buy official policy does not allow for price match of contract phones anymore . If course, you may get lucky, but that would be dependent on the store. You can price match to the full retail price of $699 from Verizon.

Sent from my Verizon Samsung Galaxy Note II

this totally depends on the luck of the draw, and the store you go to. I spoke to two seperate best buy reps at two stores, and they both told me I could price match amazon pricing for an upgrade. then I called best buy 800 number, and was told that contract cellphones can't be price matched. so basically, it's a toss up. either order from amazon.com and get your price for sure, or go to Best Buy and take a chance on getting upset cuz they won't do it.
 
why is the Note 2 still more expensive than the new S4 at Verizon?

They are trying to sell as many as they can in a short period of time. You'll still buy the note II no mater the price so why drop the price. The price will drop after the Note III comes out.