Personal experience coming right up . . . I'm a politics undergrad at the University of Manchester!
I'm in my second year, and I have always been very happy with the department (teaching etc.) and facilities. There's a limit to how much I can comment on the MA course, but as a lot of the same people will be teaching you, I'm happy to recommend it.
The university is the largest single-site university in Europe. That means that there is
- a lot of funding (and so lots of new buildings, like the recently opening Learning Commons, and the plan to spend £1bn ($1.6bn) moving the North Campus closer to the main campus)
- the largest non-legal deposit academic library in the UK with lots of computers and study spaces.
- the widest range of electronic resources of any UK academic library
- a large students union
- employers like to target it because it's well regarded and they can reach a huge number of students in one day
- a large variety of modules available for you to take, because the numbers make it viable (certainly this is the case at UG level, please check about PG!)
- an incredible variety of sports and societies on campus - everything from football (soccer) to rowing to religious societies to the baking society.
The city itself is great too - the nightlife is some of the best outside London, quite student orientated and cheap. There's lots of shopping, and great transport links to other cities and the rest of Europe (I know a lot of international students like to travel whilst they're here!). It's 2 hours by train to London, for instance, and there's a local bus that takes you to Manchester International Airport from the university & halls of residence.
The city is very multicultural - around 25% of the students and staff are from outside the UK, and the local area has a large Asian population (which is great - lots of options for curry and falafel, and I'm currently sat eating some baklava - yum!)
If you want to live in university owned accommodation (halls of residence) whilst you're here, then Manchester guarantees that you will get a place, unlike most other universities. Alternatively, you could choose to share a house with other students.
If you're planning on working whilst you're here then Manchester has a lot of employment opportunities. During my time here, I've applied for four jobs, and got three of them (and the one that I didn't was a speculative application anyway). The university offers quite a few different employment opportunities - everything from showing prospective students around the university to working in one of the on-campus bars and cafés. You can expect to be paid £6.19-£7ph for the sort of unskilled work that students normally do. In contrast, Dublin is still struggling to recover from the recession and so jobs are much harder to come by.
I have to admit that I don't know much about TC Dublin, but if you have any more questions about Manchester then I'll be happy to answer them