Em Lyon bba or Bi Norwegian bba which is the better path to lse and Private equity

Hey, 17yo French student choosing between emlyon Global BBA (FT top 10 Europe) and BI Norwegian BBA (FT top 40, Triple Crown). Long-term goal is LSE MSc Finance to PE in London.

emlyon has the better ranking but BI gives a fully English environment, Bocconi exchange opportunity in year 3, and a more differentiated profile for LSE.

Does the ranking gap actually matter from a London finance perspective? Anyone gone through LSE admissions or works in PE with a similar background?

Thanks