Only the first option will work as written. You can't say 'are prestigious at the international level'. You'd have to say something like 'are internationally prestigious.'
However, note that the two aren't completely synonymous anyway. A university could be well-regarded, but not necessarily be considered prestigious.
For example, most of the public state universities in the US are considered good schools, meaning you can get a good education and earn a valid degree and be well-regarded internationally, but they won't necessary be considered as prestigious as say Harvard, Yale, MIT, etc.
Student or Learner