FYI, Litespeed Enterprise server has a open source free sibling called OpenLiteSpeed
http://open.litespeedtech.com/mediawiki/ - performance is pretty much the same just OLS doesn't support cpanel/WHM drop in ability or native on the fly reading of .htaccess files like LiteSpeed Enterpise. OLS has a admin console field to add .htaccess rules instead. Think of it like moving .htaccess rules up into Apache httpd.conf instead.
LiteSpeed/OpenLiteSpeed static file serving performance matches and depending on how it is configured can surpass Nginx server. LiteSpeed/OpenLiteSpeed's LASPI PHP handler
https://www.litespeedtech.com/products/litespeed-sapi/php also performs and scales much better than Nginx's pairing with PHP-FPM especially for non-cached PHP requests in high concurrency environments.
With that said, it's not about what you use but how you use it too. So if you are more comfortable and familiar with Nginx, you'd use Nginx or LiteSpeed if that is more your cup of tea. Both for high concurrency work loads will need to be further tuned anyway so just switching to either without tuning won't be beneficial for high traffic sites. High traffic I am talking about 500,000 unique ip visitors/day like loads
If you use WHM/Cpanel, then easier to go from native Apache to LiteSpeed Enterprise as it has cpanel plugin support.
With that said I currently develop my own LEMP stack installer, Centmin Mod with Nginx 1.11 + PHP-FPM but I also plan to integrate Apache 2.4 + PHP-FPM and LiteSpeed/OpenLiteSpeed + LSAPI PHP combos too.
