As the economy becomes more globalized, this becomes a more salient question to many firms. There are good and bad points of using each.
Expatriates are the most likely to fully understand the needs of the firm. They will work most easily with the higher levels of the firm because they share a culture with them. However, they will have little understanding of the country in which they are working. They may be seen to favor the needs of the firm and their own country over those of the host country.
Host-country nationals will have the opposite situation. They will get along well with the people in their own country (broadly speaking) but may experience culture gaps and misunderstandings with the home offices. They may be sucked in to acting in ways that make sense in their home culture but are harmful to the firm.
Third-country nationals have less to be said for them. They are neither fish nor fowl so it may be that they will understand neither the host country nor the home offices. However, they might be seen as more neutral parties who are not automatically going to take one side or the other.