Getting response headers is easy: run curl -D- -o/dev/null -sS [url] or load the site in a browser with the networking tab open. Getting request headers is harder, because webservers don't have a way to dump this exactly as they received it. Yes, you can set them to log specific headers, but logging all headers exactly as they came over the wire isn't something I see in nginx or apache. Netcat can help here. Start it up on some unused port:

    nc -lp 8070

Now make the thing you're debugging visit yoursite:8070. Netcat will print out what headers you got:

    GET / HTTP/1.1
    Host: www.jefftk.com:8070
    Referer: http://www.jefftk.com/...
    Accept-Encoding: gzip,deflate
    Cache-Control: no-store, no-cache
    Accept-Language: en-US
    Connection: Keep-alive
    Accept: */*
    Accept-Encoding: gzip,deflate
    ...

See the duplicate Accept-Encoding header? It turned out that A was adding an extra encoding header which then made B disable gzip. [1] Once I had the raw headers as sent it was pretty clear what the problem was.

(Because the problem was a duplicated header I'm glad I didn't go with a higher level tool that might have masked that problem by storing headers in hashtable or something.)

[1] Sniffing the traffic would have been ideal, but I wasn't in a position to get in between them.