Bath or Durham?

I need to decide whether to put Bath or Durham as my insurance choice for maths. Does anyone have any information or advice? I'm awful at making decisions and may be overthinking this.

In terms of the courses and the maths departments, I'm more interested in Bath's research than Durham's (but I don't know to what extent this would impact the undergraduate teaching?) and I think a placement year would be beneficial, which Bath seems slightly better for. However Durham seems to offer a greater range of topics and a bit more flexibility. Durham is also higher in the rankings and has higher student satisfaction. I'm likely to meet the entrance requirements for both, so that doesn't really factor in to my decision.

In terms of location, I slightly prefer Durham because it's smaller but it is hard to find affordable private accomodation after first year (although the university accomodation for first year is slightly cheaper compared to Bath). I'm also concerned about Durham having a low proportion of students from low income backgrounds (basically, are a lot of people posh? Is it diverse?) and its "Oxbridge rejects" reputation. Also Bath has peregrine falcons nesting on one of its churches so... (Yes, yes, I know that isn't really important!)

I also would like to learn German, which only Durham has a course from complete beginner level (but I am teaching myself some so might manage on Bath's course if I can get enough done by then), plus I can't find the prices for students for Bath's language courses so if anyone happens to know them that'd be helpful.

This is very long (as I said, overthinking!) but the last things are societies (both have things I'm interested in, Durham has a few more that I like than Bath but both have more than I could possibly join)
and Durham is collegiate, not really fussed about that. I would be interested to know what the general atitude is towards politics in each university, are people quite involved or do they just not care?

Thanks if you've read all this. Perhaps I should just flip a coin?

I can't answer everything here, but I can respond to a few of your concerns. Research that the university is undertaking won't have much impact on undergraduate teaching at all to be honest with you. For some subjects, the research they're doing may factor into final year projects / capacity for postgraduate students, but for an integrated MMath I'm not sure how much that would be true in this case.

Student population wise, all universities will attract a wide range of people from all kinds of backgrounds, and both of the unis you're looking at are pretty big, so the net is quite wide. Yes, there may be plenty of people at Durham who've had comfortable backgrounds, but there will also be lots of those people at Bath too. That doesn't make them arrogant, or snobbish or anything else, there will be people from all walks of life whom you will not get on with.

Accommodation-wise, if cost might be an issue it is worth considering the general price range (especially for private landlords) but there will always be a range wherever you are.

There are prices for language courses? Maybe you can't find Bath's because they're free, like they are at my university to take them as an elective.

Me personally, I wouldn't fuss too much about the rankings; but my (very personal) preference would be toward flexibility and variety of course options than the industry placement.

Society-wise, I imagine you'll find that both unis will have similar kind of political climate, where the vast majority of students don't care strongly about politics, except for the students studying politics, and those who are part of the societies (often a big overlap).

I hope this helps somewhat.
MR