Both versions have the full chapters, but v1.1.1 is more polished, stable and less buggy in general.
Viewing post in The Letter - Horror Visual Novel comments
Hi Akash, if you bought the game on Steam, then it should update automatically. If it isn't updating automatically, open up the game properties (right click the game in your Library) go to the "Local Files" tab, then select "Verify Integrity of Game Cache" it should force an update if one is available.
SOURCE: https://gaming.stackexchange.com/questions/127901/is-there-a-way-to-manually-upd...