To take routing out of the picture, try changing a machine in Site A to a Class B subnet mask and a machine in Site B to a Class B subnet mask. This will put them both on the same Network ID. Then ping the machine in Site A from the machine in Site B and vice-versa. Change your Ping to use the /L switch as follows:
Note: Before changing the subnet masks, run the following pings to get a baseline performance indicator. Then make the changes.
Ping /l 64 PC_IN_SITE_A
Ping /l 640 PC_IN_SITE_A
Ping /l 6400 PC_IN_SITE_A
Repeat in the opposite direction. You should see about a 10% increase in time from 64 to 640. Then about double the time from 640 to 6400.
Note your findings. Did you see any changes in speed with these two machines. If so, there is a problem with your route tables or router configuration.
If it is not a route issue, then my next question is when the fibers were laid, were they certified by the installer for transmission quality? Do you have the correct modules in the switches for the fiber types? The modules for Multi-mode fiber are not strong enough to push light through the much smaller diameter Single-mode fiber.