among dozen of diverse applicants; what would lead you to let an (Ph.D.) international applicant to join your team? which attributes she must features to choose her instead of your domestic or past students?
A lot of variables would apply, one being how the PhD program was structured, whether scholarships were in place or the candidate was self-funded, whether there was a place on a research "team" or whether there were places on a wider research programme, and whether there was a set of targets for that wider program. Across Europe, systems vary dramatically. There is an association of PhD directors that might be able to help you with contacts and respondents - EDAMBA (contact me if interested). In my school we have a high number of international PhD students on our programme, but only a handful are attached to specific funded "teams". The criteria for the first are simply personal merit and a topic we can supervise; the second requires specific skills required for the project and is more competitive - language or quant skills may be decisive, in some cases field experience is an advantage.
Very interesting question. Based on my experience I would say three reasons:
1) They bring skills and abilities to the team that are not available among local candidates.
2) They bring contacts from their country of origin or from other countries, either with scientific groups and/or with project funding organizations, and
3) They help to form a multicultural team, which can be a strength when carrying out research that seeks to publish with a more global approach.