Story:

Sanitarium is more of a twisted psycho mind trip, Stasis is a conventional sci-fi horror story where you're all alone on a spaceship and have to figure your way from A to B and get past problems while slowly discovering the story via data logs that you find on the way.

Gameplay/Puzzles:

Both games are traditional point & click adventures with hotpots that you click on and items that you can carry around. The puzzles in Stasis feel more organically incorporated into the story, meaning there is a logical reason for what you need to do and it follows scientific laws for the most part. In Sanitarium, there are some esoteric puzzles and some weird machinery puzzles that rely more on experimentation.

Sanitarium is generally more challenging and not always in a good way. In Stasis, things make more sense. Even if it's science fiction & horror, you still use objects in ways that more closely relate to how you would use them in the real world. In both games you simply use the left mouse button to interact with things (right mouse button to walk in Sanitarium) and that's it, very simple controls for both games.

Backtracking is not a problem in either game, you never have a huge area to access in either of them. Backtracking is no issue in Stasis, the game closes off access to areas behind you as you progress and you'll only have access to a handful screens at a time. So no worries about having to backtrack through the whole ship to find a tiny item you forgot to pick up in the first place.

Pixel hunting was a bit more of an issue in Sanitarium and despite the higher level of detail in Stasis, items are logically placed where one would expect to find them.

In Stasis, there are no combat scenes like the boss fights Sanitarium has. There are only very few timed puzzles in Stasis but nothing that requires super precise timing or accuracy.

Scenery:

Sanitarium has chapters with completely changing scenery, in Stasis you're always on the same ship. Different decks looks different according to their function but the overall design is consistent, this is not a downside though as the level of detail is very impressive and there are all kinds of interesting little details and animated parts and sound effects that spice things up.

Stasis looks like "Sanitarium in Space" and the gameplay is traditional point & click material in both but Stasis tells a more straightforward sci-fi horror story that will remind you of many famous movies and games, the developers list Event Horizon, Alien etc as some of their inspirations and you'll find references to many other movies and games in Stasis as you progress through the game.

Sanitarium focuses much more on the psyche of the protagonist whereas the star of the show in Stasis is the screwed up spaceship itself and you're just a random victim that finds himself aboard that ship, trying to find a way out. Both games try to mess with your mind but Sanitarium does it more successfully by ripping you from one stage to a completely different one, making you question your own sanity. In Stasis, you just want to figure a way out of the mess around you, not the mess -inside- you. Both games are very atmospheric and if you like Sanitarium, you're pretty much bound to get Stasis because there are very few games in this style.


edit: typos