A Kohen may become Tamei to his close relatives. A Nazir may not. Why? The Shem MiShmuel says in the name of his father the Avnei Nezer that the Kedushas Kohen is inherited. It is a family kedusha. Therefore, just like he received his kedusha from the family, he may not turn his back on them, even if dealing with them would make him Tamei.
The status of a Nazir is reached purely by the individual, through his holy aspirations. It is not received in any way from other family members. He has no debt to pay and, therefore, may not defile himself to bury a family member. Similarly, to become Kohen Gadol one must elevate himself through his own efforts. Therefore, the Kohen Gadol also may not become tamei to family.
Hill Republicans call on Kerry to apologize, resign for reported Israel 'apartheid' remarks