I have now ran them both with the cover off, the old one arcs really badly and doesn't run properly. In comparison, the new one is now only arcing slightly but runs smoothly - and seems to be getting better with use.
I am now thinking that the new motor's brushes hadn't been bedded in and this caused the arcing and smell when it was initially installed. I was concerned I still had the problem and it could only be caused by a fault in the electronics controlling the motor, which I was clueless about!
On further investigation, I don't believe the motor has any electronics controlling it to go wrong. I have therefore tried running it for longer periods to see if it gets better with use.