Elsewhere in the comments here, it's mentioned that nginx doesn't yet have server push so maybe it's fair to call these naive test setups then? I'd certainly buy that HTTP/2 has more head room for acceleration and optimization but I'm curious what the difference there would be. However, it starts to sound like programming language benchmarks where the test servers aren't setup in an "idiomatic" manner.
I believe that HTTP/2 isn't opening many connections. It's opening one TCP connection and multiplexing many requests through that. This would allow for exploiting a pre-warmed TCP connection in subsequent requests. I've always felt that was a flaw in HTTP/2: with minor modifications, that multiplexing protocol could have been split out.
I'm interested to see how HTTP/2 could accelerate your modern jumbo media websites. The ones with a dozen or so tracking bugs, ads, etc. All splattered across multiple domains with ad servers that aren't quite as zippy as one would wish.