Roof or towbar

We have just made my selection for a replacement car for our V reg
Peugeot 406, which I bought second hand just under 10 years ago.

The 406 is beginning to fall to pieces - with the air conditioning
broken, the 12v power socket broken, the remote control door lock
broken and locking and unlocking the car can only be performed
passenger side; and to top it all the nearside wing mirror glass was
broken through a misjudged reversing manoeuvre by my wife, but I have
managed to gaffer tape a replacement glass into place for our
forthcoming trip to France.

Our new car will be a 13 month old Peugeot 5008 MPV, delivery in two
weeks, after we return from the Loire Valley in our dilapidated 406.

I have a roof mounted tandem carrier which is fine, and a rear end
bicycle rack which I won't want to use on the new car. What is better
for transporting bicycles (other than tandems), roof carriers or
towbar carriers?