You're looking at the world through a pinhole. A valid test of latency differences at different speeds would be between two identical NICs connected with a cross-connect cable. Set the NICs mathching speeds of 10mb, 100mb and 1000mb. This will show that there is virtually no difference in latency at the different speeds. All packets travel at the same wire speed regardless of max bandwidth being used. Once you add switches with store and forward caching everything changes. Testing latency through a switch must be done with only two connections to the switch. Any other traffic may affect the latency of your test. Even then the switch may roll-over logs, adjust packet type counters, update internal clock, etc.. Everything may affect latency.
Yes, switching from 100mb to 1gb might be faster (lower latency) due to hardware changes, different NIC, different switch, different driver. I have seen larger changes in ping latency from driver differences than any other changes; bandwidth, switches, offloading NICs, etc..
The switch would be the next biggest change with cut-through significantly faster than store and forward for single transmit tests. However, a well designed store and forward switch may overtake the cut-through switch in overall performance under high load. In the early days of gigabit I'v seen 10mb high performance backplane switches with lower latency than cheap gigabit switches.
Ping tests are practically irrelevant for performance analysis when using the Internet. They are quick tests to get a ballpark idea of what's happening on the transport at the moment of the test. Production performance testing is much more complicated than just a ping. High performance switches are computers and under high load behave differently - change in latency.
Having a slower NIC, or a NIC set to a slower speed, could actually help a server with concurrent bursts by throttling the input to the server using the switches cache. A single re-transmit may negate any decrease in latency. Usually medium to high-load traffic levels are important, not single ping tests. e.g. Old slow Sun Ultrasparc (higher latency for a single ping) outperforms new cheap gigabit desktop used as dev server when under 70% 100mb bandwidth load. Desktop has faster gb NIC, faster connection gb-gb, faster memory, more memory, faster disk and faster processor but it doesn't perform as well as tuned server class hardware/software. This is not to say that a current tuned server running gb-gb isn't faster than old hardware, even able to handle larger throughput loads. There is just more complexity to the question of "higher performance" than you seem to be asking.
Find out if your provider is using different switches for the 100mb vs. 1gb connections. If they use the same switch backplane than I would only pay for the increase if the traffic levels exceeded the lower bandwidth. Otherwise you may find that in short time many other users will switch over to the gigabit and the few users left on the old switch now have higher performance - lower latency, during high loads on the switch (overall switch load, not just to your servers).
Apples and oranges example: Local ISP provided a new switch for bundled services, DSL and phone. Initially users saw an increase in performance. System was oversold. Now users that remain on the old switch have higher consistent performance. During late night, users on the new system are faster. In the evening under high load the old switch clients clearly outperform the new overloaded system.
Lower latency doesn't always correlate to faster delivery. You mention MySQl in the 20 requests to serve a single page. That traffic shouldn't be on the same NIC as the page requests. Moving all internal traffic to an internal network will reduce collisions and total packet counts on the outgoing NIC and provide larger gains than the .04ms latency gain of a single packet. Reduce the number of requests per page to reduce page load latency.