Why does the debate over election/predestination matter?

Ascribe to the LORD, O heavenly beings, ascribe to the LORD glory and strength. Ascribe to the LORD the glory due his name; worship the LORD in the splendor of holiness. - Psalm 29:1-2

The theological "election debate" as it is usually played out dances all around and actually misses the point. One side argues to defend the absolute and complete sovereignty of God (which appears to be clear in Scripture) and the other side argues to defend a responsibility of human choice (which also appears to be clear in Scripture). Divine election actually incorporates and defends both. He foreknew and then He created: Therein lies election.

Election is declared in Scripture to be according to the foreknowledge of God (1 Peter 1:2). If it can be apprehended that God is "big" enough to have foreknown every free decision made by every human being ever born even before He created then election and creation are inextricably linked.

As it is written:

And if you call on him as Father who judges impartially according to each one's deeds, conduct yourselves with fear throughout the time of your exile, knowing that you were ransomed from the futile ways inherited from your forefathers, not with perishable things such as silver or gold, but with the precious blood of Christ, like that of a lamb without blemish or spot. He was foreknown before the foundation of the world but was made manifest in the last times for the sake of you who through him are believers in God, who raised him from the dead and gave him glory, so that your faith and hope are in God. - 1 Peter 1:17-21

If the shed blood of Christ was foreknown before the foundation of the world, then the free choice of Adam to sin was foreknown also. Why shed the blood of a sacrifice before any offense is committed? If the shed blood of Christ was foreknown to be for the sake of "us" who are believers in God then our belief was also foreknown prior to creation. If one wants to argue that God sovereignly "makes" or "enables" our individual belief then they must also argue that God "made" or "enabled" Adam's disobedience in the same way, because it was all foreknown prior to creation.

A sovereignty that is unable to be sovereign over the free choices of it's creation is no sovereignty at all and is certainly beneath attribution to Almighty God.

The practical implications of the doctrine of election are:

1. God is both sovereign and good. He knows absolutely everything that is ever going to happen and He is working all things together for the good of those who love Him so...the only safety is to trust and obey Him.

It is the LORD who goes before you. He will be with you; he will not leave you or forsake you. Do not fear or be dismayed. - Deuteronomy 31:8

2. We actually can and must choose to trust in the Lord with all our hearts. Our choices have consequence and matter. We cannot be born again against our will nor can we effect it ourselves:

For thus said the Lord GOD, the Holy One of Israel, “In returning and rest you shall be saved; in quietness and in trust shall be your strength.” But you were unwilling... - Isaiah 30:15

3. Once one is born again by calling on the name of the Lord, that one is predestined (through sanctification of the Spirit) to be conformed to the image of the Lord:

For those whom he foreknew he also predestined to be conformed to the image of his Son, in order that he might be the firstborn among many brothers. - Romans 8:29

From everlasting to everlasting there is no choice, action, or intention of any entity in all of creation that can take the Lord God by surprise. Nothing is hidden from His sight. He knew humanity would fall into darkness if given choice, He knew Jesus would ransom humanity, He knew who would respond to His grace, He knew who would reject it...and then He created, thus bringing it all to pass. This is election and it is rooted in the infinite omniscience of God.

Oh, the depth of the riches and wisdom and knowledge of God! How unsearchable are his judgments and how inscrutable his ways! “For who has known the mind of the Lord, or who has been his counsellor?” “Or who has given a gift to him that he might be repaid?” For from him and through him and to him are all things. To him be glory forever. Amen. (Romans 11:33-36)

First, let's address the premise of your question:

one way to summarize it is that we are debating whether God decides that the sinner decides to come to Christ and accept Him as Lord and Savior and repent, or whether the sinner decides that the sinner decides to... So what difference does that make?

This is a false dilemma. Regardless of which model of God's action vs. free will dynamic one believes, subjectively we are conscious when we make the decision to follow Jesus. (Of course, we are leaving to God's graciousness on how He will deal with those who don't receive a good gospel presentation.) Therefore, the debate itself does not make a difference practically.

HOWEVER, the Doctrine of Election itself matters a lot since NT talks about it a lot, even though the content of the doctrine itself differs depending on the denomination. Why does it matter? One answer by Jonathan Landry Cruse is given in an article adapted from his recent 2019 book: 3 Points about the Doctrine of Election Every Christian Needs to Know:

• Election is a big doctrine since it shows the sovereignty of God. Even if human free will has a role, God still has foreknowledge of it and God's freedom is greater than our own freedom since He created our freedom.

• Election is a beautiful doctrine since it shows the goodness of God. Even if human free will has a role, God loved us and chose us first, then He gave us the grace to support our own choice for Christ.

I’m going to give the simplest answer I know. After I became a Christian in my mid-20s, it only began to slowly dawn on me, after the event, the wonder of why God would save a sinner like me, and how he did it. I had left a group that denied mainstream views of election/predestination, claiming knowledge about God and Christ was the essential factor in individuals deciding to become Christians. But there could be no assurance of salvation because you had to keep doing all the right things till the end of a future millennium, and then you should get to live forever. That was a religious system – man-made – a heavy burden.

That burden fell off when I repented of my sin while looking only to the finished work of Christ on the cross, not my own level of Bible knowledge or what I did. I had no idea about any doctrines of election and predestination. Now I do, decades later. So, it’s simple to agree that such doctrinal understanding is not necessary for salvation. I don’t know any believer in that who even thinks it might be. The doctrines of justification and sanctification are also involved, so the matter is truly deep, and some people love to go into the depths of such theology, but for those who know they are chosen and loved of God, that appreciation can only come after the event – the miraculous event of God bringing one to newness of spiritual life.

Conversely, there are those who argue about doctrines, trying to justify their religious stance, and because the doctrines of election, predestination, justification and sanctification are presented so differently by so many Christian (and non-Christian) groups, debates rage. This is so dishonouring to God! Once God does his work of grace in justifying a contrite sinner, then let that person study God’s word and hear sound gospel teaching, to discover the wonder of it all. Of course nobody is ever going to be able to explain it all entirely to everybody’s satisfaction. That’s because nobody can fully explain God; only God can explain God, and he has chosen to reveal so much of himself to redeemed sinners, but not everything. Even in the glory, when our myriad questions have been answered, God will still remain over and above us. Eternity won’t exhaust the quest to know God more, because he is God and we are his creatures.

So, my answer boils down to what might be a simplistic statement: After the event of one being brought to spiritual life, we can agree with Romans 3:4 – “Let God be found true, though every man be found a liar”. (Linked to Psalm 51.) We collate all that God has revealed to us in his word about the matter, and wonder in amazement with doxologies of praise, continually seeking to understand more. But for those who view the matter as a spiritual boxing ring, taking on all-comers, pity help them.

The pastoral reason this debate matters so much is because of the related doctrine of assurance (which itself is intimately related to justification by faith alone). To put it bluntly, if our salvation depends on the eternal decree of God, then our assurance is based not on our own performance but entirely on the grace of God. If salvation depends even partially on us - e.g. on our choosing somehow, or on our ability to keep God's commands - then our assurance rests on our own performance. And if that is the case, then it leads to questions such as "How can I ever know I've done enough to be saved?"

This was a key and live debate at the time of the Reformation. So, the Church of England's 39 Articles includes this as part of Article XVII (On Predestination and Election):

As the godly consideration of Predestination, and our Election in Christ, is full of sweet, pleasant, and unspeakable comfort to godly persons, and such as feel in themselves the working of the Spirit of Christ, mortifying the works of the flesh, and their earthly members, and drawing up their mind to high and heavenly things, as well because it doth greatly establish and confirm their faith of eternal Salvation to be enjoyed through Christ, as because it doth fervently kindle their love towards God...Source

Contrast this with the Council of Trent, session on Justification, 38:

No one, moreover, so long as he exists in this mortal state, ought so far to presume concerning the secret mystery of divine predestination, as to determine for certain that he is assuredly in the number of the predestinated; as if it were true, that he who is justified, either cannot sin any more, or if he do sin, that he ought to promise himself a certain repentance; for except by a special revelation, it cannot be known whom God hath chosen unto Himself. Source

This is the reason why the debate on election is not esoteric. It may seem to be like trying to calculate how many angels can dance on the head of a pin, but it actually has ramifications for the Christian life.

Further reading on the Doctrine of Assurance:
Wikipedia
Gospel Coalition