I've noticed in various threads that many people rank Oxford's BCL and Cambridge's LLM programs above those of LSE, KCL and UCL.

Why is this the case? It seems that LSE in particular (as well as a number of other schools in UK) offer specialized programs whereas Cambridge and Oxford offer only a general 1 year program without the opportunity for specialization.

Am I missing something? Is this just a "prestige" thing?

What are the career prospects for someone with a general LLM versus a more specialized degree?

In my opinion, a lot of it is the "prestige", in fact. It takes some doing to get admitted to Oxbridge especially.

There are good arguments for and against a specialized degree. If you have a specialization in human rights, for example, don't expect to get a job in banking and finance. At the very least, you would have to have a convincing explanation for having studied human rights and then attempting to abandon it for a "brighter" future in business law practice. If you have a general LL.M., however (perhaps you took one course in banking and finance and one in human rights among other legal disciplines), you may be more diverse and less restricted in applying for jobs.

If you know what kind of law you want to practice and you're willing to accept and weather the market, then a specialization may be a benefit in interviews. I don't think you will confront questions about why you want to practice human rights law, if you have specialized in it in a LL.M. Your degree will demonstrate your interest and commitment to the field.

[Edited for a past/present participle problem.]

I think much of what you say is true. Oddly enough though, I've been admitted to Cambridge and wait listed to LSE. Still trying to figure out whether that's a good thing or not.