The packets are all TCP packets, which carry the HTTP protocol, the request method doesn't change the network layer's response time.
It will change on request-to-request basis depending on the size of a request, but that's not determined by the request type.
You can send more data with post than get, but this doesn't mean they respond faster, it's a separate issue.
The speed at which the HTTP server can process and return a result is on the server you're using, and likely to be so negligible it's not worth mentioning.
The speed at which the result comes back from the server depends on what resource the HTTP server is processing, if it's calling a PHP file that takes time, then it's going to take time...
There isn't a clear difference in the packets... this is a GET request over SSL:
00907f8252f7001e4fe86a93080045000028
0bb2400080067380ac100167adc22064c51a
01bb66ccad148448d84850103f05bde90000
And this is a POST request over SSL:
00907f8252f7001e4fe86a93080045000028
0c0640008006732cac100167adc22064c511
01bbe538c0df8621dc6150104042248c0000
There isn't exactly a lot of involvement of whether the string inside the TCP packet is "GET" or "POST," the network looks at it, says "oh, you're TCP, Huh? Well, off you go then." It doesn't care.
Any delay outside of normal network traffic is soley due to processing on the sever level, or on the code it's working through.