Let me briefly (or not) sketch some of the major theological difficulties C.S. Lewis created for himself in choosing to make Aslan, not merely a Christ-figure, but the very Person of Christ.
First, Who is Christ? He is the Word of God, the only begotten Son of the Father, the image of the invisible God. Christ can only be understood in His relation to the Father.
Jesus, when He was among us in the flesh, talked constantly of His Father. His first recorded words refer to His Father; He spoke to Him on the Cross; He spoke of Him the morning of His resurrection. The Son became man to reveal to us the Father's love -- and to reveal the Father Himself to those who did not know Him. All that Christ has is given Him by the Father, and He refers all glory back to the Father.
Can this be said of Aslan? Yes, he's the son of the Emperor Across the Sea. But he shows no particular interest in this fact. In The Lion, the Witch, and the Wardrobe, I'm pretty sure he only mentions the Emperor in connection with the unthinkability of disobeying his father's law. In short, Aslan is in no sense the revelation of his father; if his presence (I've tendentiously called it meddling) in Narnia has anything to do with doing his father's will, he keeps it a complete secret.
Further to this failure to reflect the relationship between Divine persons, what price the Holy Spirit? If the existence of the Father is manifested in an off-hand and unserious way, as a remote giver of obscure laws, the existence of the Holy Spirit is kept (as I recall) a complete secret. Aslan reveals only Aslan; practically speaking, he is a Unitarian.