As I prepare the 1.20 update (which will follow this devlog post by probably half an hour or so), I've compiled a list of changes to expect in hard mode. 

The following is a list of all differences (aside from enemies being harder) in all of the worlds on hard mode:

Barbie Horse Adventures: More obstacles added.

Chrono Trigger: No significant changes outside of harder enemies.

Earthbound: No significant changes outside of harder enemies.

F-Zero: More obstacles added. Mute City has been changed to look and sound like Big Blue.

Fall Guys: More obstacles added. 

Final Fantasy VI: No significant changes outside of harder enemies.

Garfield Kart: More obstacles added to Lasagna Park, and more oil slicks added to Harry chase scene.

Glitchwerks: Low chance of encountering glitches as random encounters.

Inscryption: Changes to rewards some events offer.

Kirby: Enemies move faster on the map.

Juglim's Domain: No significant changes outside of harder enemies.

Legend of Zelda: Many more enemies roam the map.

Lisa: There are now random battles on all maps.

Mega Man: Select screen is recoloured slightly. Tellies now move much faster.

Ogre Battle: Brand new enemies can be fought and hidden treasure locations changed.

Pac-Man: Power-up pellets have been removed.

Pokemon: Town is recoloured slightly. No significant changes outside of harder enemies.

RPG Maker 2000: No significant changes outside of harder enemies.

SimCity: No significant changes outside of harder enemies.

Sonic the Hedgehog: Many more enemies roam the map.

Super Mario: Overworld map is recoloured slightly. Enemies remain unchanged, but time limit is much more unforgiving.

Zombies Ate My Neighbors: More zombies roam the map and survivor locations have been changed.