For the most part the transfers are the same as the individual discs, but there are a few differences and improvements. On the original part 1 disc (released in 1999) Annie's death is uncut and Pamela Voorhees' death is trimmed. On the box set disc it's the official R rated theatrical print with Annie's death back to its cut form and Pamela's death restored. Over at horrordvds.com the reviewer mentions that "the transfer for the original film is a bit brighter now than it was before in the single disc release. It is also a little less vibrant, but it is hardly a distinguishable difference. The new transfer for The Final Chapter looks a smidge softer than the single disc release, but again it is nitpicking."
On the original Part IV: The Final Chapter disc (released in 2000) there are a few missing audio cues. During the opening credits when "The Final Chapter" explodes through the hockey mask you're supposed to hear a stinger, but it's gone. There are at least one or two other examples of this happening on the original disc. On the box set disc these cues have been restored.