We have never said that God "empowers" some and leaves others to perdition. God ENABLES those whom He chooses.
You still have this idea that you chose to be saved. You couldn't have, unless God had enabled you, by His Holy Spirit opening your spiritual eyes and ears to see the Kingdom of God, and to hear the Word which imparted faith to believe. Your "choice" was due to His prior regeneration of your spirit IN ORDER THAT you could see, hear, and believe. Until He did that, you could not have chosen to believe. This isn't "programming" or "robotics". It is God sovereignly working on your heart, so that you can believe.
You still have never answered my question: What is it that makes one person choose Christ, and another reject Him?
Roget's first synomym for empower is enable. Your semantic wrangling aside, you still make God a respecter of persons concerning salvation, which scripture denies.
"What is it that makes one person choose Christ, and another reject Him?"
In general, I would suppose the same thing that make one person choose any path over another: their will, their priorities, etc. We can't read men's hearts, so we should probably leave that to the Lord.
In scripture, several different reasons are revealed for men believing but not choosing to accept the conditions of salvation. Among them: fear of men, desire of approval of men (John 14:42-43).