SPDY is this new, cool, fast protocol created by Google that “replaces” HTTP (the first draft of HTTP 2.0 is using SPDY as the working base). It is supported in all the major browsers – yes, even Internet Explorer – with the exception of Apple’s Safari.
TL;DR: Varnish lacks support for SSL and SPDY. Nginx handles it just fine, and has very fast cache with either memcache or disk storage (ramdisk). Both can serve stale cache if your backend is down. But Nginx can not write to the memcache storage directly, it has to be done by the application. Also, Nginx can not purge the cache itself, without you compiling your own package.