The latter felt a lot more isolating and stressful. Partly because of having to live in London, with its expensive housing that will be far away from the main campus in South Kensington when you move out of student accommodation. Partly because the students there are perpetually stressed overworkers with terrible study-life balance. Partly because Imperial focuses only on science and technology courses, so attracts mostly a certain type of person that I personally would rather not be stuck in such a tedious monoculture with. And partly because of the gender imbalance which is also due to this, it felt exceptionally weird to be in a university that's so male-dominated.
If Birmingham offers what you want, I would choose that for all the opposite reasons of what I wrote above. It has a beautiful campus too, lots of open green space and lovely redbrick architecture.
Also don't worry about the exact name of your degree. Employers won't care.