Connected in series each motor should in theory get half the supply voltage, which means if you series them on 6V they are only getting 3V each. This is well below their rating so they will be slow and in practice there will be differences between the two, even though they appear identical, which means one will run faster. The amount you describe does suggest there is a significant difference, but you don't say what sort of motors they are or if they are connected to physical loads.
If you want them to run at 6V then you will need them in parallel for a 6V battery and in series for 12V. But I don't recommend series connection, partly because you can get some odd effects as the motors affect one another, but more for the simple reason that if one fails to an open circuit the other will stop too, so you have an unnecessary single point of failure.