Hey, I can't really comment about Newcastle, but I study Mech Eng in Exeter and it's pretty great. The first year is a blanket year for all engineering sub categories, then the second year is specific to your sub category, and the third year you can choose a few modules. I've finished my first year now, we had a group project to design and manufacture a Pelton wheel generator which was entertaining.
Exeter itself is ana amazing city, but it depends what floats your boat. I'm into Mountain biking, climbing and surfing so Exeter is pretty perfect. The campus is really nice, really modern facilities all around and VERY well kept gardens. It keeps winning various green awards for having the best natural spots in the country. The Engineering building itself could be better, but you learn to love it. I've only been there a year but I feel religiously connected to that building <3
Exeter Uni has a pretty massive international scene. There's a whole building nearly as big as the main forum + library dedicated just to international students, for them to study in!
I suppose how important the extra £4000 a year is, if you're budget is tight, that will probably make your mind up for you.