Don't know much about Stats programs, but I have spoken with some well-known profs and they've given me a good list of departments that have been historically strong in probability:
- Stanford (Stats or Math)
- Berkeley (Stats or Math)
- U British Columbia
- ETH Zurich
This list isn't in any particular order and, as you can see, only contains schools that teach primarily in English. You'll need to look at faculty interests at each school to determine whether or not it's a good fit for you.
Re: Stats vs Math, if the school allows you to apply to both, why not? It should raise your chances of getting in. Otherwise, unless your application is very strong, I might apply for Stats as (anecdotally) those programs may be a bit easier to get into.