You're looking specifically at timing - when the packet goes in, when it comes out, when the server returns a response, and when the proxy releases it.
Assuming you have VLANs labeled "internal" and "external", the following minimal TCPDUMP syntax should get you what you need:
tcpdump -lnni internal:nnn host [host IP filter] [and other filters]
tcpdump -lnni external:nnn host [host IP filter] [and other filters]
With the differences you're seeing, the source of the delay should be fairly observable in the captures.