@bristolorbath the best uni is the one you love, surely. You have to live there for three years or more and you need to enjoy that if possible.
For maths, of those three, Bath is certainly the top choice. That offer is punchy tho – is he likely to achieve it? (obvs it may be a walk in the park for him.) I think it’s important to bear in mind that maths in particular at uni is a big big step up, and Bath (among others – but there was a thread recently about Bath) demands a lot of its maths undergraduates.
Yes (yes) any uni is asking a lot of its students, or should be. A degree should never be easy. But if you are studying Eng lit or even MFL, you can find your level a bit more easily than with maths, which is a bit more sink or swim. DS found that with A level – when he got it, it was great, but often he was sitting looking at his super maths-whizz mate who was so far ahead he was working on in the text book just for the fun. (DS got a B and never planned to do maths at uni btw – but I think the analogy is there.)
The other thing is, even if he thinks, well, I have a good insurance (ABB is I would imagine very achievable for him), it's worth looking at how that works if he needs to take it up – does he get guaranteed accommodation? Is there likely to be any choice? That can be a factor with insurance offers (and with clearing) but it varies from uni to uni.
I don’t really know about the jobs market, but I cannot imagine that Bristol vs York will make much difference there. Bath tho esp with its industry connections is winning there again.
Lastly (sorry long post!) you mention a significant investment – yes indeed uni is that for sure. But bear in mind that housing costs in Bristol and I believe Bath are very high. I mean I have heard York mentioned as ££ as well; but I personally know three YP who have been at uni in Bristol in the last three years, and they have all paid around £10k for a room in a shared house. That's £30,000+ (as the figure is going to go up over the nest couple of years for sure) you need to find (bc some of the halls in Bristol at any rate are not much cheaper) before they have eaten or got a bus or bought a pair of trainers. You may well be all over this in which case apologies, but it was just the ref to finance that made me think. Mind you, as I say, I gather York is much the same.
All the best to your DS whatever he decides.