yury123:
Unfortunately, we are admissions experts, not immigration attorneys so we'll just comment on the choice between two great programs!
It sounds like Tuck is the better fit if you want to end up in the US and can figure out all the immigration. It's easier to recruit within the same country in which you are pursuing your MBA.
The LBS name is stronger overall than the Tuck name. Yes, Tuck has a great reputation and a very loyal alumni base, but LBS is more internationally recognized. Tuck does very well in placing its students at all of the consulting firms you mentioned, plus more. The program feeds well into the type of work one does as a consultant, especially on the data science side.
Let's see what type of money (if any) you get from LBS. That might help make your decision easier.
You have a lot of variables going on here, so how would you rank/weigh them? We can easily dive into any of the above with greater scrutiny, but it might all be for naught if it's nothing something that factors heavily into your decision.