Optimal way to get to a hedge fund - exit from MBB or AM?

Hi guys, lately, I've been contemplating the next move in my career and I am looking for advice. The story is as follows: In October I am starting my last year at the university. I've just completed my Visiting Associate program at BCG at one of the CEE offices and received a full-time offer. Also, I have contacted several people in my network and I have a possibility of joining some of the biggest asset management firms in my country (most of the times operating under some insurers or banks) as an equity investment analyst.

My main goal is to get to the hedge fund industry (some value shop), preferably in the UK. The question is whether (after graduation) I should accept the FT position with BCG or I should move to the Asset Management firm. The problem is that, although those forementioned AM firms are well respected in my country, they are almost surely no-names abroad, so getting into BCG will surely give me a brand name and some valuable experience, but experience not as much profiled for the work in a hedge fund as the experience from an asset management firm.

Some more info on my background (might be helpful): BA in Finance, MA in Psychology, both from no. 1 university in the country; completed 2 internships in PE shops and 1 internship in the fixed-income mutual fund.