Thank you for your replies.
Of course, I did have a look at other threads before posting this one, including the econ sticky in postgrad section. Warwick's mentioned there as a good option, which I don't doubt it is, but I didn't find it compared to Birkbeck which I suspect might be not be worse than Warwick.
Reputation's one thing, which the university acquires through a long time and the quality of translating that research reputation into quality of teaching in a taught postgrad course might be another thing altogether (I've heard some nasty things about unfair exams etc, can't tell if it's just a rumour or a fact).
Besides, I'm a bit scared off by the communication of the Uni of Warwick - from its rather poor website (uncomparable to BBK, at BBK you can even have a look at most of the teaching materials, modules syllabuses, etc. even if you are not yet registered), to the long time it takes the admissions/registry dept to reply to an email, etc. Although this has nothing to do with the research/teaching directly, it tells you something about how the institution works and whether it cares for its (potential) students.
I did my first degree (5 yrs, approx. an equivalent of an MA) in Public Economics and Administration, in my home country Slovakia, so it can be considered a no name poor quality uni, although with good marks, Dean's Award for my thesis and helping out in a Slovak econ think-tank. I also spent a year as an exchange student at a German University in Osnabruck, but it was not very different from what I experienced at home.
This year, did a Graduate Diploma in Finance at Birkbeck to get something more credible into my CV and to try out the UK/US system for myself at first, and, as I expected, it was a completely different world - the teaching, the content, the exams, the schoolmates, everything. It was simply great.
Now, I've got an offer from Warwick and an expected offer (expected distinction, in that case you get an offer to continue with them) from Birkbeck. In the future, I'd like to go on to a PhD.
I guess, with so much bad experience (from Slovakia and Germany), I'm just too scared to leave something that I know is good (BBK), though not with as much reputation (but is the rep difference so great..?) for something which looks good in rankings but I know nothing about it personally and hear different things about (Warwick).