The adult version adds a scene of Taiki and Elisabeth sharing a bath near the end of the story which ends in a short sex scene. This adds approx 5k~ish words to the existing script and 2 extra CGs.
The adult content isn't particularly explicit and it's not hugely plot-important so it can be skipped if you're not interested in it. It's just a cute bonus for people who like erotic scenes in their love stories!