I have used both on the same the car. Used to have a Thule roof rack it’s ok carrying two bikes very hard to get a third on. The towbar on the otherhand is very easy to load very quick to install I have a Thule Tow bar rack with a single lever to install takes secones. If you are leaving the bars on all the time then it will be a little less faff.
I found that in the current conditions the salt get’s on the bike weather on the roof or attached to the back so there is no difference there.
My car is a diesel passat and putting bikes on the roof would knock 20mpg compared to not having them on, and on the back about 10 – 13mpg less than I’d get without. Bars on their own around 5mpg and the extra noise!!
For me I can’t see ever moving from the tow bar solution it just works and Mrs F can load her bike on it which would never have happened with a roof rack 🙂 I think the only better solution is VW Transporter 🙂