Now, do the voltages of the Arduino board and the FDTI interface need to match? I understand that the "5V" board is clocked at 16MHz and therefore mightn't run properly when powered by a 3.3V interface. But is there anything wrong with programming a "3.3V" board with a 5V interface?
I think the opposite is true. A 3.3v serial converter module/cable/chip should work fine with any arduino 5vdc board, as 3.3vdc is still a 'legal' logic HIGH voltage on a 5volt board.
However using a 5vdc converter module/cable/chip should not be used with a arduino 3.3vdc board as the higher voltage can damage the input pins on the 3.3vdc board.