Switching to LEDs: 12v LEDs on existing transformer or remove transformer and use 240v LEDs - Which is better?
I would stay with 12V if possible.  

Because LEDs draw very little current, a minimum load requirement may be a factor if there are any electronic parts such as a dimmer or a transformer.  

For general residential lighting 12V would be the best choice.  Running at higher voltages for incandescent, halogens and especially for LEDs is unnecessary and probably does more harm than good.  Compare it to using a sledge hammer for hanging a picture.