I am studying Maths at Bristol and I am really enjoying it. In terms of worldwide ranking - Bristol is 55 and Manchester is 51 - so not much difference. Internationally, they are on par I would say. In terms of how it is viewed by employers - they are similar as well. Those in the Maths arena know Bristol is better. The course is great. I would say some parts are easier than I thought it would be but not all of it! Overall, there is a lot of homework compared to A Levels - but that is probably the same whichever uni. One thing that surprised me was I thought initially all my lectures would be in the Maths building but in reality they are all over the place in different departments - which is both good and bad.
But going back to your question. What is funny is I had Manchester down as well, but decided to go for Bristol because it was nearer to home. If having easy access to home is important, then it is a no brainer - Manchester. I went home once during reading week which was great. I am glad I was only 2 - 3 hours away, if it had been much further, I may not have gone home. I really needed to just be home after a few weeks and it was nice to go home and decompress.
In terms of life - Bristol is a fantastic city to live in. There are so many societies as well. I have been to Manchester before and both are great cities in general. I agree with the lasanya above - accommodation is expensive. I got in as an insurance choice(Warwick was my first), so it was a lottery to get accommodation, but got fantastic catered halls - and yes it is £8k-9k a year for this year (though food is included) and I have already secured next years accommodation with 4 others ( you have to do it early in Bristol!) at just under £9k for the year which doesn't include bills. I think Manchester is also expensive, but Bristol is a tad pricier. It is expensive, and most students I know are like me, relying on parents. I know I am blessed in that respect. If you have the financial support then go for it. Without parental support and relying solely on maintenance grant - I would avoid both Manchester and Bristol and go somewhere cheaper altogether!
Good luck.