As a general rule, the axes are arranged to where the operator stands in relation to the machine. This makes the left/right axis the X axis and the front/back axis the Y axis - the main reason for this is that is the way many CAD/CAM softwares display/produce their image/Gcode. But it does not have to be this way and you are free to choose whatever orientation suits you best.
To change the axes, either way you mention is OK but I would just swap the cables (you may also need to make changes to the way your limit switches are configured, depending on how they are wired).
Tweakie.