When it comes to people, it is important to be sensitive, yet authentic. It is a delicate balance.
Some people are insensitive in the guise of being authentic. Some are too sensitive to the point of being not authentic.
If you are trying to appoint someone to a role and want him or her to perform at their peak then being sensitive and authentic will have the highest chance of success. Sensitive will make the person feel respected; authentic will keep the foundation of trust and integrity sound.
If you have to choose between sensitive or authentic then choose authentic but it need not be either/or.