Srhoades is correct again!
It is the circuitry of the root hub that controls the speed capabilities of the USB connection.
USB 1.1 = 12Mbps
USB 2.0 = 480Mbps.
1394 Firewire = 400Mbps.
I have yet to find a USB cable, no matter the age, that did not work as well with USB 2.0 as it did with USB 1.1 as the pinout is identical.
You can even replace a PCI USB 1.1 card in an elderly Pentium II Win98 machine with a new USB 2.0 card, and the driver will enable the card's chipset to allow full throughput. Then other parts might bottleneck the data stream....but it won't be the USB port itself.
Unless the cable is broken, you shouldn't have a problem. Remember that USB 2.0 is meant to be 100% backwards-compatible with all facets of USB 1.1.