Both are variety shows with actors/performers that a Korean audience would have been exposed to (so, people who are famous or did something notable).
However, the overall vibe (everyone is trying to get to the top, forming and breaking alliances, trying to collect points, and also just the amazing character dynamics, betrayals, and mishaps) are the same in both. They both have a group of people staying in a confined area/close together for a week and know that they likely wouldn't meet outside of the show.
Biggest difference is that New World DOES NOT eliminate people every day/episode, while Time Hotel DOES. This causes Time Hotel to be much more high-stakes and somewhat sadder overall.