I have one laptop with both Ubuntu 12.10 and Mint 14 installed side by side. They connect to the same router using the same power line network. The Ubuntu speed is measured at 5.36Mb/s the Mint speed is measured at 4.89Mb/s. So Mint is indeed slower, but I wouldn't consider that one test to be all that significant statistically, it could easily be accounted for by other factors. To get a true picture I would have to repeat the test many times over at many different times of day and average them out, and I don't think it is worth it for a difference 0.47Mb/s.
But if you want to criticise Mint over its speed capabilities, there is one huge difference - start up. From pressing enter in the login dialog to a loaded desktop appearing: Ubuntu - 5 seconds. Mint - 30 seconds, 6x longer. Now that may be worth investigating, but not the tiny difference in recorded internet speed.
Fujitsu Lifebook AH532. Intel i5 processor, 6Gb ram, Intel HD3000 graphics, Intel Audio/wifi. Realtek RTL8111/8168B Ethernet.Lubuntu 13.10,Ubuntu12.10 (Unity), Mint16 (Cinnamon), Manjaro (Xfce).