EASY
-Game has frequent checkpoints
-You can save at Cassette Recorders any time you like
-Enemies do less damage with attacks
-Enemies move a lot slower (about half the speed they move at on Normal)
-High Regenerating Health (you recover health quickly, and get somewhere between a third and half of your half of your health back through regen)
-Enemy AI is set to easy mode, they have a lot harder time spotting you and are much easier to shake off from chasing you. Sometimes enemies will purposely even not attack you to give you a chance to get away.
NORMAL
-Game has checkpoints, less frequent than easy however.
-You can save at Cassette Recorders any time you like
-Enemies do the normal amount of damage with attacks (more than easy, less than madhouse)
-Enemies move at normal speed (about twice as fast as they move on Easy)
-Low Regenerating Health (you recover health at a much slower rate than Easy, and get somewhere between a fifth to a fourth of your health back in regen)
-Enemy AI is set to normal mode, they do more scouting and harder to lose than easy. Enemies will not spare you if near you like they do on easy.
MADHOUSE
-Game has no checkpoints at all.
-You can only save at Cassette Recorders, and only if you have a Cassette Tape. Cassette Tapes are a new item, they take up an inventory slot and there are finite of them. You need to locate and use them to save.
-Enemies do a higher amount of damage than normal, and are more resilient to damage
-Enemies move a bit faster than normal (I don't believe twice as much, but come after you faster)
-No/minimal regenerating health (needs a bit of clarification)
-Enemy AI is set to hard mode, they can spot you a lot easier and are far more aggressive.
-There's more antique coins in Madhouse Mode, and they're all in completely different locations to the other difficulties. The other difficulties have 18 antique coins, Madhouse Mode has 33 coins you can find, and all in trickier to find places.
-On-top of this, there are more bird cages in the game and new upgrades that aren't in the other difficulties. The bird cages also aren't all set in safe places, they are now spread apart around the levels. There are new 'special ability' coins you can purchase that give you big stat boosts, they take an inventory slot but give you a big boost in stats and are exclusive to this mode.
-Item locations are remixed to the other modes, where there's items in some modes there's no longer any, and trickier locations for items.
-There is remixes in enemy spawn points and numbers. There are certain encounters that are made to surprise you if you played the other difficulties.