I'd rather post this as a comment but it's pretty full already up there.

This benchmark routine by Ike Devolder is probably one of the most fair and detailed that I've come across in the past few years comparing Litespeed and Nginx:

https://blog.herecura.eu/blog/2020-06-16-openlitespeed-vs-apache-vs-nginx/

Some of the confusion is re: Litespeed vs. OpenLitespeed, but for this purpose it doesn't really matter since the biggest difference with Nginx is LSAPI, the PHP processor, rather than using PHP-FPM, and since OLS supports the same server-level caching that Litespeed does...

One of the best things about Ike's review is that he doesn't definitively say one is "better" or "faster" and instead talks about different components of either stack, while monitoring resources.

The TLDR for 2021 is probably something like this:

1. Both Nginx and Litespeed serve static assets extremely well
2. Litespeed as a stack scales higher than Nginx currently, partially due to HTTP/3 support... but 99% of websites probably will not notice this since we are talking about insane traffic levels, which almost never reach the origin server these days due to things like CDNs or remote MySQL servers, and since HTTP/3 is not fully integrated into the internet yet... in fact, even in Ike's own tests he seems to have tested both internally (not over i.e. UDP) which further reinforces this point since HTTP/3 is UDP-only. However, regardless of protocol, Litespeed does appear to scale to a higher level than Nginx... keep in mind, this is not the same as saying that LS delivers requests "faster" than Nginx, because real world requests at a typical traffic level are probably indistinguishable in terms of speed/response times. It does mean that i.e. a shared hosting environment with 500 cPanel websites would probably scale better using Litespeed... so it makes sense why that seems to be Litespeed's main target.
3. Litespeed appears to use more RAM memory than Nginx in general
4. Nginx appears to use a lot more CPU than Litespeed at high traffic levels
5. TCP (not Unix socks, the Litespeed default) performed a lot better, and this is true for Nginx as well, since it avoids disk I/O... so, using default Litespeed settings is still a bad idea

Anyway, best not to get too detailed, since software changes all the time really. The next version of Nginx will probably support HTTP/3, among other features. I do wish that the Litespeed guys would let the unique quality of their software speak for itself, and chill out on the aggressive (inaccurate) claims being made... but most of their web hosting partners probably benefit from that hype, which is maybe why not many people are questioning the claims being made...