The Time and Guardian tables suggest that they are about on a par for Law. Newcastle has slightly higher entry requirements, which is to be expected for popular subjects like that because of Newcastle's 'party city' reputation which may be a bit overstated.
Leicester city isn't as famous and didn't have loads of trendy bars and restaurants when I was there in the late 90s but what it lacked in that it makes for in terms of the university campus, which is pleasingly compact and interesting, and the halls of residences which are often old Edwardian houses with mostly 60s extensions to them. There are quite a few clubs in the city for its size but the excellent students union and halls events also more than adequately cater for entertainment.
The University of Leicester used to be part of the University of London and is part of the 1994 group of mid-sized (in the case of Leicester) to smaller universities. It doesn't fall in to an obvious category of 'redbrick' or 'plate glass' either - it's just one of the best examples of a campus university in the UK that there is because it realises that people often don't want to live on a campus but want a close knit feel off campus. As it has a traditional and yet modern feel to it, it seems to equally attract people from public schools, grammar schools and comprehensives although there are obviously more of the latter 2.
Comedian Bob Mortimer chose to study Law at Leicester. I think that it is still taught in the grand Fielding Johnson building, which adjoins the impressive hi-tech library.
If Newcastle's Law School is older then it may be very slightly more respected for Law with some employers but I think that will be partly down to their incorrect assumption that Newcastle is significantly older as a university, which it isn't, certainly as an independent university.
The degree grade you get will be the most important thing. If you are studying somewhere that you like then it will be more enjoyable trying to get a good degree grade- visit them both.
If you're going to study somewhere with more than its fair share of 60s buildings (which both have), I say go to the place that has the best 60s buildings (as well as the best new buildings)- Leicester. The university is based in a nice park and there are university botanical gardens in Leicester as well. Leicester University is the best of all worlds whereas Newcastle, frankly, can smack of 'didn't get in to Durham' (even if many Leicester applicants also applied to Durham).