Most people are familiar with the notion of the stick and carrot, the idea of using a combination of rewards and punishments to induce desired behavior. In the context of a roleplaying game, this can be applied as a dungeon mastering technique. Player characters are given rewards for going along with the plot of an adventure, and often forced into adventures by some kind of threat or other external impetus.
The thing about choosing between whether to apply the stick or the carrot to your player characters when designing an adventure is that it is in fact a false dichotomy. The truth is that there doesn’t have to be a difference between the stick and the carrot.
The key is to remember that the “stick” should involve making the players’ experiences with the game more interesting and exciting, while the carrot is there primarily to reward the characters. When things happen to make the characters’ lives unpleasant, the players are (hopefully) getting to have fun—thus turning the stick into a carrot for the player.
Of course, this is not true of every stick that can be applied. A stick that removes or alters something vital about the character, without having discussed it with the player ahead of time, can be a deal-breaker. Finding a way to put pressure on the character without it also upsetting the player can be tricky, but it’s ultimately the most rewarding way of applying “the stick”.