I have some DVDs that have had a UPC sticker placed on top of the printed one (directly on the packaging, not on the wrapping material). Should I be using the UPC from the sticker or remove it and use the UPC underneath?

I would say to use the original UPC and not the sticker,, Plus you can check each of those two numbers in data base and see which one is currently used.  if none go for the one on the box, because after wrapper has been removed ,, there goes the UPC code, ,
Plus I'd say the extra stickered code is for store inventory only and is done for their cataloging purposes and you'd find that the stickered code is only used 'regionally' and not nationally as we currently use the codes for identifying DVD product around the world.

OOPs edit, just reread your post I see you said on packaging and not on wrapper..,
So'll I go back to my first suggestion, check data base- if none used use the 'stickered' one instead.

A lot of releases I get from DVD Pacific have those stickers on the packaging. I always remove them (which is sometimes not that easy).

Batman Begins was rereleased without the comic book and therefore with a different back cover. The UPC however remained the same as for the original release For sales purposes a sticker was placed on the plastic wrap.



In general, I always remove the stickers as well and use the original printed UPC.

I've had quite a few anime DVDs from Bandai with new UPC stickers stuck over the old UPC, when they have re-released them at a lower price. I usually use the new UPC due to the price difference.