Here's how I say they are both true... I think that God draws all people to Him in different ways. In other words, I think that God initiates a connection with each one of us. (Don't quote me on this, but there may be a point where God no longer reaches out, if a person has repeatedly chosen to reject God and wants nothing to do with God...but that's a topic in and of itself.)
At the same time, when we respond to God and believe and receive the gift of salvation (or 'redemption' since you prefer that word), it is through Jesus. In other words, believing that JESUS paid the price for us, and it's not through our own efforts. As the bible says, the only "work" is to believe/ have faith. (John 6:29) And part of a saving faith is having a change of mind and heart, and choosing to follow Jesus.
At odds? Really? Why can't both passages be true?

What exactly prohibits God from tugging on your heart string (its called a Conscience) that stops Jesus statement, "I am way....." from being true? The scriptures point out that Jesus is God incarnate, thus.......God and the Christ work with one accord.
There are steps to salvation. The bible clearly states that salvation from sin is only in Christ (Acts 4:12).
What are the steps necessary to man to pass from a sentence of spiritual death ( eternal separation from God) to life in Jesus Christ the Savior? Jesus is "....the author of ETENRAL SALVATION to all who obey Him." -- Heb. 5:9
Indeed Jesus stated, "I am the way, the truth and the life; no one comes to the Father but through Me." -- John 14:6
In the same book of John we find this statement, "And the word was made flesh, and dwelt among us (Jesus), and we beheld His glory, the glory as of the only begotten of the Father, full of grace and truth." -- John 1:14 To clear things us with no ambiguity whatsoever. Who was the Word? "In the beginning was the Word, and the Word was with God, and THE WORD WAS GOD." -- John 1:1
Why does God tuck on your conscience? God wants everyone to be saved (1 Peter 4:6, 1 Tim. 2:4) The Word is Jesus, The Word is God......again why can't both passages be true?
How can one be drawn unless one first believes? And if you believe you will follow the advise of God in relation to salvation.
Gods Advise as to how to be saved? Step 1. Faith/Belief, one has to believe that Jesus is the Christ, the Son of God...i.e., God incarnate (John 16:16, John 6:69) That Jesus was sent from heaven as the only Savior from sin (John 8:24)...that "He who has the Son has life; he who does not have the Son does not have life." -- 1 John 5:12 One has to accept that you are living a life of sin and are without hope if you first do not believe.........no one can trust themselves to find salvation (Rom. 3:8-23) Once you believe you must ask the question, "What must I do.........."
Step 2. Repent or turn away from your old sinful life (Luke 13:3) 3. Confess to the deity of Jesus the Christ, that He is indeed the Christ of prophecy, sent from heaven to establish His eternal kingdom .......as confession leads to salvation (Rom. 10:9, Matt. 16:16, 1 Tim 6:12)
4. Be born again.........through the symbolic act of water baptism, born of the water and the Spirit. This symbolic act is where one dies and is born again, where one comes into spiritual contact with the Blood of Christ to cleanse one of all sin, as the old man dies (2 Col. 2:11-14, 2 Cor. 5:17) and a new life begins when one arises from the water like Jesus arose from the grave (Rom.6:3-5,17-18, Gal. 3:26-27, Rev. 1:5) For the forgiveness of sin (Acts 2:38, 22:16, 1 Peter 3:21)