Both are lousy in my opinion. Neither really perform that great, but are sufficient for the standard listener who isn't attune to picking up flaws/ not used to superior quality of more expensive headphones. From what I have noticed is that the sound performance from both haven't really changed, it was more an aesthetic change between the new and old.
Also, neither are really that comfortable in your ears, I have heard complaints from all sides. I just used the new ones for the first time because my other headphone was missing its cushion. I didn't find it comfortable at all.
If you want better sound quality, comfort, and possibly noise reducing/canceling qualities out of your headphones, you will not be satisfied with the ones provided with Apple, old or new. I use Sennheiser CX300s and love them ($60-70 suggested retail). The ones included with iPods are meant to just to be cheap add-ins to the package since all players nowadays come with headphones. They both have about equal sound (mediocre at best) and are not that comfortable, so it is difficult to really say which is better or worse.