Is God less glorious for choosing us rather than having us choose him?
The Bible teaches that we are dead in trespasses and sins since the Fall (Ephesians 2:5). It says that the mind of the flesh does not submit to God's law—indeed it cannot—and those who are in the flesh cannot please God. But you are not in the flesh, you are in the Spirit, if the Spirit of God dwells in you (Romans 8:7-9).
Paul divides the world into two groups: those who are in the flesh and those who have the Spirit. And he says that those who are in the flesh (that is, everybody apart from the new birth) cannot please God (Romans 8:7-8). And in 1 Corinthians 1 and 2 he says that the natural man cannot receive the things of the Spirit because they are foolishness to him.
Now the only question left after a group of texts like that is whether or not that inability, that "cannot," is blameworthy or not, whether it gets us off the hook or puts us deeper on the hook.
I think the Bible is pretty clear that the corruption of our own hearts, being so profound that it incapacitates us to do good, intensifies our guilt rather than relieves us of it. My inability to do good apart from the Holy Spirit is not an exonerating inability. It is an inability that is rooted square in my rebellion. And my rebellion is so great and so strong that I cannot see Christ or hear the gospel as beautiful. Rather, it is a stumbling block or foolishness; and until I'm called, awakened, born again, I cannot see it as beautiful. And that "cannot" is a culpable blindness, a culpable deafness.
So what I believe about free will is that I am free to do whatever I please, and what I please is to sin. Therefore I'm going to be damned by my free will. I must be rescued from the bondage of my free will in order to see and hear God for who he is.
Does that make me an automaton or diminish the glory of God? I don't think so, because what God does is come to me and free me from the bondage of my blindness and deafness and hardness so that, finally, I become rational and can act as a truly free human being.
Paul says in Galatians 5:1, "For freedom Christ has set you free. Do not submit again to a yoke of slavery." So true freedom is being set free from the bondage where what we wanted to do destroyed us.
Now, after new birth, what we want to do is God's will. And in that freedom we act rationally according to what really exists. Thus God gets great glory both for the liberation that he performed on our behalf and for the praises that we now bring him, not as people who are enslaved to sin, but as free people who are seeing the world for what it really is.
God gets glory in being praised for being seen for who he really is. Previously we couldn't see him for who he really is because we hated it so much. And now we do see him for who he really is, and therefore our praises are rational and clear and good, and he gets maximum glory for our obedience, faith, and praise.
So I don't believe in free will if you define it as man's ultimate self-determination. I believe free will as, "you can do whatever you please." Before you're born again what you please is self destructive and sinful. After you're born again, what you please is the will of God. So in both cases you have free will in that definition.
But what most people who are sophisticated, theological, and philosophically-oriented mean by free will—over against what I believe—is "man's ultimate self-determination." And I don't think there is any such thing, especially since the Fall when our self-determination became always in bondage to sin and therefore self-destructive.