This may be ignorant and please correct if I am off base but given the same physical medium isn't sending 2k across the network the same cost whether you are at fastE or gigE? Given the network is not saturated?
However, to make things work over copper I believe that gigE has a larger minimum packet size so it's not quite apples to apples on pings (latency).
For bandwidth, the max size (w/o non-standard jumbo grams), is the same, around 1500 bytes, and gigE is pretty much linear, you can do 120MB/sec over gigE (and I have many times) but only 12MB/sec over fastE.
For any transfer there is the per packet overhead (running it through the software stack) plus the time to transfer the packet.
The first packet will, in practice, transfer very close to 10x faster, unless your software stack really sucks.
The second packet is a 1/3rd size packet so the overhead of the stack will be proportionally larger.
And it matters _a lot_ if you are counting the connect time for a TCP socket. If this is a hot potato type of test then the TCP connection is hot. If it is connect, send the data, disconnect, that's going to be a very different answer.
Not sure if I'm helping or not here, ask again if I'm not.