It depends on what you wish to achieve as they have their strengths and weaknesses.
Apache is great for running small sites. However, it is not great for many concurrent connections, requires a lot of RAM. Can stop working when the load is high because it is process based.
Nginx is great for handling a lot of simultaneous connections on the same server and consumes a little less memory than Apache because it is event based. However, it is not that good for customization and also does not read ".htaccess".
LiteSpeed also uses the event-driven approach as Nginx. The benefit of it is that it also has some strengths as Apache - you can use ".htaccess", "mod_security", "mod_rewrite" and many more. You can easily transit from Apache to LiteSpeed. However, it is commercial.
If you are willing to buy a license, it is always great to have official support available and I would recommend choosing LiteSpeed. It has strengths from both Apache and Nginx. In another case, I would go with Nginx.