Asset Management vs Investment Banking for exit opps into value-based hedge funds

Hello everyone, I am a South American student in my final year at a target uni in London and I currently have 2 full time offers and I am stuck and do not know which one to choose. The offers are:
1) A full-time offer from an elite boutique (Lazard/Rothschild) where I would be doing a mixture of restructuring and M&A in the London office
2) A full time-offer at an asset management fund for a rotational graduate programme in PM tracks and Equity research tracks, also in the London office. The fund is large with more than €400bln in AUM and more than 16 locations worldwide.

My career goal is to eventually become a PM at a hedge fund here in London or possibly in NY. I am really not sure what I should choose. On the one hand, what I would be doing in AM would be much more similar to a HF job as it would be investing although with a more long term perspective, on the other hand I am not sure how possible the transition from AM to HF actually is (especially here in London) and I am scared to be stuck at a large bureaucratic organization (possibly less clear career path than in banking) with few opportunities to join the hedge fund industry.

As far as the banking offer is concerned, I think it is the safest as it seems like you cannot go wrong with banking as your first job, but I also think that the exit opps here in London are not as good as in NYC and thus I could be putting in all those hours for two years without even having the option to eventually leave for a good HF role with a PM track. Moreover, I would enjoy banking less than investing and I would have to put in many more hours.

To sum up, my questions for you guys are:
1) How easy is it to transition from AM to HF in London? Is it easier or more difficult when compared to doing so from banking?
2) Assuming I do not succeed in leaving AM, how do compensations in AM in my 30s and 40s compare with banking? Would I be earning significantly less in AM?
3) What would you do if you were in my shoes given the that I am sure that my long term goal is to be a PM at a hedge fund?

Thank you very much in advance!