People utilize many different stances in kettlebell sport. Each has pros and cons which I will outline. Generally, a vertical jump and barbell jerk are performed with a narrow stance. The main reason behind this at you are trying to move yourself or something vertical, so you apply your force vertically.
Here is a video of me performing 16 kg jerks with a narrow stance. Note the angle and height of the arrows. These arrows indicate the overall direction and magnitude of all the reaction forces (resultant vectors) for each leg. You can see that most of the force is applied vertically, this force is transferred up my body into the kettlebells efficiently. You are unlikely to be able to perform long cycle in this stance, which will limit its carry over. Additionally, some people find it hard to rack the bells with straight legs in this stance.
This is a video of 16 kg jerk with a wide stance. In this video you can see the arrows move inwards along the line of my legs. This indicates that I’m applying force horizontally, which may increase my stability but reduce my efficiency. However, it is often easier to rack with straight legs and perform long cycle with this stance. We can also look at deadlifting to get a bit more background on this topic. The sumo deadlift is performed with a wide stance compared to a conventional deadlift for a number of reasons. Commonly, people find sumo deadlifts easier on their back. The increased horizontal forces may help with force/form closure of the SIJ and allow the back to stay in a more advantageous position. The wider stance reduces the height of the lockout in the deadlift, somewhat counterbalancing the loss in vertical force.
In the end an individual’s structure will somewhat dictate what stance works best for them. You just need to be aware of the pros and cons of each stance. In an ideal world you would use a narrow.
Bonus video of 32 kg jerk, notice how much longer the arrows are.