The difference of the two you say?
Speedtest.net uses a pure flash-based approach, and drops the top and bottom 5% of your tested speed. Why? Because the first instant of testing is typically slower due to the requirement to establish a connection. Then there's often a sudden burst which is typically irrelevant to your speed. Speedtest.net is more useful for a total-throughput test. It's often handy for gamers to test what the typical speed of their connection is. (After all, they are using UDP mostly which is connectionless, so there is no establishment of a connection.)
Testmy.net uses a pure HTTP based approach, and does not remove any data. Why? Because almost all of the typical users network traffic is over HTTP, which requires the establishment of a connection. (Downloads, webpages, style-sheets, images, etc.) Testmy.net is much more relevant to testing your total connection throughput. Basically giving you a true establishment of how websites should download.
Thanks,
EBrown