What is the difference between proxy_cache_ and fastcgi_cache?
The difference between the two is the protocol used to communicate with the backend.
fastcgi_cache is related to the FastCGI backend protocol. It caches output from FastCGI connected backends.
proxy_cache is related to backends that use HTTP as the backend protocol, and it caches output from HTTP connected backends.
fastcgi is used in far more setup assistance for nginx caching than the proxy_cache. You are more likely to run into websites that offer substantive articles for configuring fastcgi caching than for proxy_cache so thats a pro.. to use fastcgi