You have certainly asked a BIG question on the Magento Forums!
Have you read through what NGINX has to say about it?
https://www.nginx.com/blog/nginx-vs-apache-our-view/
Here are some practical considerations
https://www.digitalocean.com/community/tutorials/apache-vs-nginx-practical-considerations
One of my favorite articles from Sonassi hosting
https://www.sonassi.com/blog/mythbusting/why-shouldnt-i-use-nginx-for-magento
So what is your question? How many users are you serving? How many orders per hour?
All those go into your answer. Of course many hosting companies are starting to support NGINX out of the box so again. Why wouldn't you go with it? How often are you restarting your Web server that you need to worry about changes? If you are in fact that busy why don't you already have two web servers load balanced? Then you can restart one and then restart the other later