Not totally sure I'm qualified to answer this (since I work for LiteSpeed), but I didn't want your thread to go dead. The biggest reason people use LSWS is that it has performance at least as good as NGINX while also remaining Apache compatible (which makes it control panel compatible and easy to set up).
As for the caching, I've never seen benchmarks comparing any of them. The functionality should be pretty similar, though I'm not that familiar with NGINX's caching. (I know more about Varnish and LSCache.)