The pixel perfect mode replicated what the designers and developers would have seen as they were making the game. (retropool.com)
Append mode allows you to beat the original game before having the option to start a New Game + with the added content, while Perfect mode lets you play through the game with the inclusion of the new content from the beginning. (popgeeks.net)
There are three display modes to choose from: CRT filter, 4:3 mode, and pixel perfect mode. (retropool.com)