I would rather be able to pause the world instead of being able to silence the world because I would have an Infinite amount of times to do things that I want. If I forgot to study for a test and the test is on that same day then I would be able to pause the world and study for it or look around somewhere for the answers and then I could unpause the world and take the test. If I didn't get enough sleep one day and I'm super tired in the morning I would be able to sleep more if I just pause the world. Also being able to pause everything around would still be making the world around me silent because no one would be able to talk, it would be just another blink of an eye to them so while I'm studying or trying to get more sleep or while the world is paused the world would just keep going like nothing has ever happened.

Something bad that could happen is if I pause the world and I die after pausing it due to something crazy the world could be stuck paused forever until something just unpauses.

Also, Astronauts in space would not know what's going on they would be trying to communicate with someone on earth and wouldn't be able to because the world is paused.