Use Cherokee Instead of nginx in Front of Varnish to Get HTTP 1.1 Optimizations?
Solution 1:
We debated this as well when putting in our backend cache layer, we are also using nginx but with squid and a JVM that serves content.
If you aren't using any functionality that is unique to nginx you could switch, we had already built a couple nginx modules.
You should consider what the actual overhead of that connection setup is vs the end-to-end request. For us when testing it was always <2ms even reading an asset from memory cache took more than that to respond (>5ms).