Should my toilet flange sit on top of the backer board or the tile of the floor?
The toilet flange needs to be on top of the finished floor. Meaning the bottom edge of the flange needs to be on the same plane as the toilet. So if your toilet sits on the tile, the flange needs to be on top of the tile too. The spacing of the toilet exit "horn" and sealing surface is designed for this height.

almost all plumbers agree, here are some sources:

http://www.terrylove.com/forums/showthread.php?51976-Toilet-flange-height



if you have it lower than the finished floor you risk leaking toilet water (the water is the best part) into the floor or worse, in-between the tile, sub-floor, backer board. This is because the wax ring was designed only to take up the air gap, not to provide a "tunnel" or extension of the pipe/flange/toilet horn.