Bocconi, HSG or SSE for undergrad?

Hello. I recently got admitted to Bocconi BESS, St. Gallen and awaiting reply from SSE Business & Economics (I will most likely get in). Which of these schools will position me best for IB/PE? I am Swedish and my budget fits all these schools, though I of course wouldn’t mind spending less. I am Swedish, but do not want to work in the long term in Sweden. In Europe London would be preferable but the most ideal is NYC (I imagine internal transfer is the easiest way to get a position there). I feel tired of Stockholm and have lived here all my life, but I am thinking of going to SSE because it feels easier to get top positions since I am Swedish and the university is highly regarded in the country. Later on I could transfer to London/NYC. Would Bocconi/HSG provide a disadvantage for me or open up more opportunities? More people go there so it feels harder to stand out, though I would appreciate a change in environment.

Would greatly appreciate tips!