Philip
I am not an advocate of plastic pipe usage, but advantages can be:
Smooth long radius bends used in routing plastic rather than elbows used in copper cause less pressure loss in feed pipes. The lack of necessity for elbows means less joints, therefore less likelihood of joint leaks developing in future - that's probably what your plumber meant. Copper joints, if made correctly, with correct pipe support and allowance for thermal movement will not "inevitably leak". If between floors, the pipe can be routed through holes in the centre of the floor joists rather than along notches in the top - better for the joist and less likely to suffer fixing nail damage in future. The flexibility of the pipe allows for thermal expansion - important over long runs. Vibration from the shower pump will be better absorbed by plastic rather than tranmitted around the house by copper.
From experience of poor plastic pipe installation I would recommend:
Make sure that joints are accessible if at all possible. Make sure pipe is supported in line with manufacturer's instructions. Do not accept the "washing line" type support where the points of support are two wide and allow sagging of pipe. This leads to air locks - a real pain in shower territory. Try to impress upon the plumber the need to avoid air locks by choosing a considered route (rather than just the easiest). This may cost a bit more, but will make shower maintenance in future far more practical. If he doesn't understand this then walk away.
Guess I've just convinced myself to go plastic in future!
HTH
Phil