Nat res group (chemicals focus) at top BB (GS/MS) vs MBB (McK / Bain) PE team for corporate PE (TMT/HC) exits?

Hi,

I am debating between starting at a strong BB (GS/MS) in a non-ideal group (natural resources) versus at a MBB (McK / Bain) within their private equity practice, from the perspective of optimizing exits into European UMM / MF funds after ~2 years.

I am most interested in exiting into a technology / healthcare focused fund and I reckon I'd be able to get exposure to these at the MBB, while at the BB I'd work primarily with chemicals, bit of energy and some broader geography coverage. I have no interest in exiting to an energy / infrastructure focused fund and I am afraid the natural resources experience would pigeonhole me into these.

Funds I'd be most interested in include the both the top-tier, more consultant friendly UMMs (e.g. Bain Cap, EQT, H&F) as well as the traditional US MFs

Other context:
-The BB offer is not in London but a strong tier 2 city in Europe. I am not quite at a fluent level in the local language / don't speak any other major European languages apart from English fluently, which could give me a good opportunity to reach fluency during the analyst years
-I have interned at a MBB and EB before, performed solidly at both albeit I feel a slight natural inclination towards consulting

(Cross-post from PE forum)