Warwick is the W in COWI: Cambridge, Oxford, Warwick, Imperial. These are recognised as a tier of their own within UK mathematics. My uni is in the tier below that and, sincerely - keep reading! - with all respect B’ham is in the next tier. (DH is a Maths professor; I am in STEM.)
This is mainly to do with research power, although it has had a knock on effect for the strength of the UG cohort and made UG admissions highly competitive. Depending on your DD’s professional aspirations, it may be easier for her to launch with a good degree from Warwick.
That degree will be harder to earn, although I always get a good feeling at Warwick and the students look happy on the whole. The ones I have known enjoyed the place.
However B’ham is a lovely campus with a fine Maths programme. It is a perfectly good launching pad for many careers and probably a less demanding course, therefore less stressful. B’ham is a terrific city.
PPs are correct that it’s a question of what fits best with DD’s personal goals. I also value applicants’ intuitions when they visit prospective universities. Perhaps your DD will gain insight by doing that. Eg Warwick is a campus uni in the middle of nowhere. Students largely make their own fun. A huge array of clubs, societies, etc. B’ham has a major city with much to offer on the doorstep. (As well as clubs and societies). Many DC will strongly prefer one or the other.