It is the latter, not the former that reveals the inner working of our heart, the orientation of our conduct, and our true attitude towards ourselves. One who has high regard for others need not deprecate ones own abilities, gifts, talents, or choices. Indeed, a healthy and accurate view of oneself, of both ones strengths and weaknesses reveals itself in the strength to value, even honor the gifts and abilities of others. The failure to do so is not only a failure to recognize the value represented by the achievement of others, but it also reveals a depth of insecurity that underscores a truly self-centered attitude and the behaviour by which it is marked.
Jesus walked in humility, and that humility was not bred in insecurity, but rather in the absolute knowledge that though "He existed in the form of God, He did not regard equality with God a thing to be grasped, but emptied Himself, taking the form of a bond-servant, and being made in the likeness of men." The man who drove the currency exchange out of the temple with a hastily assembled whip was no wimp. Neither was the man who washed his own disciples feet. It was precisely because He was secure in the Identity given him by His Father that he could do so, and teach those who would follow Him the way by which they might share both his attitude and His service.
ref: Phillipians 2:6-7, Isaiah 60:1-2a