AFAIK only phones that have a serial number beginning with '5K' are refurbished. Those beginning with a factory number starting with 8 are straight off the manufacturing line.
A white box replacement does not imply refurb. The white boxes are just phones, either new or refurb, that are specifically set aside for warranty replacement so that stock levels of new phones for sale do not affect Apple's ability to take care of its current customers. Whether a given Apple Store's stock of white box replacements happen to be new or refurb is pretty much luck of the draw as far as I have been able to tell. I had to have my 3G replaced 6 months (in December) after I bought it on "opening day" and the store I visited gave me a non-5K unit, and not even because I asked.
I have yet to hear of anyone getting a 3GS replacement that is a refurb. It's probably too soon for us to be seeing refurbs out there, especially given that stock levels are still tight for those looking to purchase. It seems to me that it took a few months after the intro of the 3G for 5K serial numbers to start showing up on service/white box handsets.
Honestly, though, I'm sure you would be happy with either. Apple refurbished products are given all new externals, so there should be no visible scratches or dirt or funny smells or anything like that.
For all intents and purposes, it is brand new, or at least appears so. And, frankly, between all of the handsets that I have had, I prefer my refurbished 3G one the most. All my retail phones have had problems or imperfections of one sort or another, but this refurbished one has been great. I suspect that the ones that get refurbished have more personal attention applied to them during the refurbishment process than any of the phones ever did going through the overseas manufacturing plants.
I would readily accept another refurbished phone again in a heartbeat.
-- Nathan