One of the elements of modern (often Evangelical, but sometimes Catholic) spirituality that I find most foreign is when people talk about Christ as being "my best friend." It seems an even more familiar form of the relationship suggested by hopeful missionaries, "Do you have a personal relationship with Jesus Christ?"
It's possible to err in either direction on these things, and I make no representation that I am a perfect Christian, but I don't think of myself having a "personal relationship" with Christ, certainly in a "best friends" kind of way. The ways in which I would normally envision Christ are not guy-next-door, my-buddy-the-savior kind of images. Christ the King, enthroned in eternal splendor into union with whom all Christians wish to enter for life everlasting. Christ Crucified, pouring out his blood for the sins of the whole world. Christ Risen, triumphing over the reign of death which had doomed humanity since the Fall. Christ in the Eucharist, kneeling before the glittering monstrance in which the Body of Christ forms the center of a sunburst of golden rays, with the crucifix above and the tabernacle behind.
This is not to say that I see Christ as distant. But while not a sparrow falls without the Father knowing it, you can hardly expect a sparrow to understand God, much less consider himself God's friend. God knows us better than we know Him, because we are understandable to Him in a way that He is not to us. I wouldn't say that I feel distant from God. Indeed, the reality of God is as foundational to my ability to understand the world as are the non-material qualities of Good, Justice, Mercy and Beauty which spring from Him, and as basic to life as the physical laws and order of creation.
Though in many ways a classical liberal, in personal as in political life, suspicious of too much power concentrated in one person -- Christ is the king to which my knee bends eagerly, the perfection which deserves utter love and obedience, the authority which is at the same time absolute and freeing.
Certainly, all this represents a relationship between persons. Christ is one of the three persons of the Trinity; we are persons made in God's image. Yet I find it hard to think of it as a "personal relationship" in the sense that I take the phrase to be meant. And it certainly is not what I would think of as a "best friend" relationship. When I look for Christ, my gaze is naturally upward. I don't picture throwing my arm around His shoulders and asking, "How's it going, buddy?"