Visa Sponsorships US vs UK - International student, no citizenship at either

Hello all, 

I am a Year 13/ Senior in High School, and am in the process of applying to Uni this year. I wanted to know about the differences in the likelihood of getting a visa (for IB/ BB/ M&A but any advice appreciated) as a fresh graduate. 

- Indian citizen, will have PR in Hong Kong

- Native in English, and would speak Spanish (C1), Hindi (B1), and Mandarin (HSK 5) by the time I graduate

- I am a girl, if that makes a difference (some say it does, some say it doesn't)

UNITED KINGDOM 

• Oxford: Philosophy, Politics and Economics (PPE)
• LSE: Politics and Economics
• UCL: PPE
• KCL: Political Economy
• Warwick: PPE [have offer already]

UNITED STATES 

• Barnard: Thinking of applying as I like the 2+2/ 3+1 tie-up options with CC
• Princeton: AB Economics
• Dartmouth: BA Economics
• Northeastern: BA Economics
• Columbia-Science Po Dual BA: Financial Economics at Columbia GS, Politics & Gov at Science-Po

HONG KONG (not fluent putonghua speaker, no cantonese)

• HKUST: BBA Global Business
• HKU: BBA IBGM, BBA Business

EDIT: I know this question has been asked a lot before, but I wanted to know from the perspective of a non-citizen of both (other posts are about US citizens in the UK or vice versa) and as someone not yet at uni (flexibility to go to either)