I won't say that league tables are completely irrelevant, but I put it to you that any league where the standards change so drastically from year to year that all 6 of your choices have dropped out of the top-20 is probably more than a little amateurish in the way they collect data and decide which parameters to judge their ratings on and how to balance them... I would go :/ at them. I would even go

!
(In fact, I know they're a joke: every academic I've spoken to laughs out loud at the notion that the work they submit for those research assesment exercises gets read, and, as far as teaching assessment goes, the teaching observed is too few to be representative of the university, so, on the whole, the rankings they get are based on the reputation of the particular academics at the departmental level, and the university's clout, influence, friends in high places, and the budget and muscle fuelling their PR machine at the institutional level. However, you didn't ask if the league tables are representative, you asked whether they matter, so I'll get back on-topic now

)
You're lucky, because on practical courses like engineering you've got other ways to gauge how good a course is: check the department's links with industry, which companies they collaborate with, whether they're doing research for them, if they send students off to placements at any big-name engineering firms, etc. For instance, someone I know who came to Leeds to do automotive engineering told me he chose it because his department have a team which competes in some nationwide universities' Grand Prix-type thing. I think he got to work on the racecar during his MSc even. I don't know specifically what you should be looking for, but I hope you get the kind of thing I mean.
All this is assuming you want to work as an engineer after you graduate, of course - if you don't care what kind of job you do then go to whichever you liked the most, as they're both pretty well-regarded unis so you'd be allright with a degree from either.
As for your Maths and Engineering alternative, in general I'd say that in general joint-honours courses really are harder, and I imagine that you'd miss out on courses which would be helpful to you as an engineer because you'll have your Maths courses to take instead.
M0KUJ1N said:
Of course the irony is that due to supply and demand, the "hardest" courses such as maths, physics and engineering are the ones with the lowest entrance requirements.
Riiiight... so all of us with non-science degrees are feeble-minded peons who couldn't be bothered to do a "real" course?

Rather than taking the "difficulty" of maths, physics and engineering courses for granted, have you considered the possibility that science-based courses
aren't difficult, but simply
seem difficult to those people doing them because they're of sub-standard intellect, having gotten lower grades in school, whereas those smart people who got decent grades managed to get into one of the more competitive humanities or social sciences courses?
I'm just kidding by the way, some of my best friends are feeble-minded pe-... er, I meant science graduates!
