Well, in short, it depends. When it comes to this question, the answers provided by the experts are not as straightforward as one might expect. It all depends on the type of activity that you perform.
For instance, if you like to practice sports where the risk of an ankle sprain is high, just like basketball, you should opt for a high-top shoe. Moreover, you should wear this type of shoes whenever you are recovering from an ankle injury, or if you are prone to sustain injuries of this sort. If you want to get all the protection that you can, it might be a good idea to also invest in ankle braces.
However, some studies indicated that people that were involved in dynamic sports did not necessarily benefit from high-top shoes. Even more so, scientists have shown that, at the end of the day, the strength of your ankles is more important than the type of shoes that you are wearing.