Where They Agree
Salvation is God's work of grace from first to last, and not a human achievement: neither side teaches that anyone earns it.
No one turns to God unaided. Since the fall, grace must go before any movement of the will toward God; the two sides state this in terms, in the doctrine of total depravity on one side and of prevenient grace on the other.
Justification is by faith, and faith is the receiving instrument, not a work that merits: both sides confess this against any doctrine of salvation by human merit.
The death of Christ is of infinite worth and fully sufficient: neither side limits the value of the cross itself.
Scripture is the court in which the argument is heard: both sides argue from the same passages, Romans 8 and 9, Ephesians 1 and 2, John 6 and 10, and both take the argument to be settled by exegesis, not by authority alone.
Where They Disagree
The ground of election: unconditional choice resting in God alone, or election of those foreknown as believers in Christ. Substance
The design of the atonement: a death intended effectually to save the elect, or a death that made salvation possible for all and is applied on believing. Substance
The nature of calling grace: a call that unfailingly creates the faith it commands, or grace that genuinely enables a response it does not coerce and that can be refused. Substance
The perseverance of believers: those truly regenerate cannot fall away finally, or a true believer can fall away finally and perish. Substance
The phrase free will: freedom from coercion, which both sides grant the fallen will keeps, against freedom of contrary choice under grace, which only one side asserts. Part of the public disagreement is carried by this difference of meaning rather than by doctrine. Terminology
Subject by Subject
Human nature and sin
Classical Arminianism
No claim stands on this subject in this record.
Classical Calvinism
The fall left every faculty of human nature corrupted and the will in bondage to sin, so that no one can turn to God until grace first makes the dead sinner alive.
The nature and extent of the atonement
Classical Arminianism
Christ died for all people without exception, and his death made salvation possible for every hearer; it becomes effectual in those who believe.
Classical Calvinism
The death of Christ is of infinite worth and sufficiency, and was intended effectually to redeem the elect, whose salvation it actually secures rather than merely makes possible.
Disagreement (substance): Both sides hold that the death of Christ is of infinite worth, sufficient for the whole world. They divide on its intention and effect: one side holds that it was designed effectually to save the elect; the other, that it made salvation possible for all and is applied to those who believe. The division is over what the cross was sent to accomplish, which is substance.
Justification by faith
Classical Arminianism
No claim stands on this subject in this record.
Classical Calvinism
Justification is God's forensic declaration that the sinner is righteous for the sake of Christ's righteousness imputed to him and received by faith alone; it is distinct from, and never grounded on, the believer's inherent renewal.
Agreement (substance): Both sides teach justification by faith, and both state it as God's act received by faith alone. They divide on the instrument's place: the Calvinist claim gives faith as the instrument that receives a righteousness reckoned to the believer, while the Arminian statements place the same faith inside a covenant relation God accepts for Christ's sake. The shared affirmation is large, and the difference under it is real.
Election and predestination
Classical Arminianism
God elects to salvation those whom he foreknows will believe in Christ and persevere, so election is conditioned on foreseen faith that grace makes possible but does not coerce.
Classical Calvinism
God elects individuals to salvation unconditionally, not on the basis of foreseen faith or merit, so that the decisive difference between the saved and the lost lies in God's eternal purpose.
Disagreement (substance): One side holds that election rests on God's free choice alone, with faith its fruit; the other, that election is of those whom God foreknows will believe. Both ground the answer in Romans 8 and 9, and both call election an act of grace; the difference is where the condition stands, and that difference is one of substance, not wording.
Disagreement (substance): The Calvinist claim is stated of individuals, whom God elects by name out of the mass of humanity. The Arminian claim is also stated of persons, but as persons in Christ whom God foreknows as believers. The disagreement is not whether election reaches persons, but on what it rests when it reaches them.
The call of God and human response
Classical Arminianism
No claim stands on this subject in this record.
Classical Calvinism
The Spirit's effectual call unfailingly brings the elect to faith; grace in this work is not finally resistible, because regeneration precedes and produces the human response.
Disagreement (substance): The two sides describe the same call in contrary terms at its decisive point. One holds that the Spirit's call to the elect cannot finally be resisted, since it creates the faith it commands; the other, that God's calling grace is real, necessary, and sufficient to enable faith, and can be resisted and refused. Everything downstream, perseverance included, is ordered by this difference.
Grace and free will
Classical Arminianism
The grace by which God calls sinners is real and necessary, and it can be resisted and finally rejected; God does not save by overriding the human will.
Classical Calvinism
No claim stands on this subject in this record.
Agreement (substance): Both sides agree that no one comes to God unaided: the Arminian claim states it in terms, that since the fall no one can turn to God without grace going before. They divide on the shape of the help, whether grace restores a freedom that may still refuse, or effects the turning itself. On the inability itself the agreement is real, and it is stated here because the disagreement is so often misdescribed as if one side taught unaided ability.
Disagreement (terminology): The phrase free will does different work in the two traditions, and part of the famous disagreement is carried by the phrase rather than by the doctrine. In the Reformed usage the will is free when it acts without coercion, and bound when it cannot will the good; in the Arminian usage freedom includes a real power of contrary choice under grace. Both sides deny that the fallen will turns to God unaided; the words free and bound are not used in the same sense on both sides, and a reader who misses that will misplace the real disagreement, which stands on grace and election.
Regeneration and new birth
Classical Arminianism
Since the fall no one can turn to God unaided; prevenient grace goes before every good movement, restoring a measure of freedom so that the gospel call can be answered.
Classical Calvinism
No claim stands on this subject in this record.
Perseverance and assurance
Classical Arminianism
It remains possible for a true believer to fall away finally and perish, so the warnings of scripture address real believers and perseverance is conditioned on continuing faith.
Classical Calvinism
Those whom God has effectually called and regenerated can neither totally nor finally fall away, because God preserves them, ordinarily through the very warnings and means of grace scripture sets before them.
Disagreement (substance): One side holds that those truly called and regenerated cannot fall away finally, because their perseverance is God's own keeping of them. The other holds that a true believer can fall away finally and perish, and reads the warning passages as addressed to real believers in real danger. The disagreement concerns what God has promised to do for those who believe, and is substantive.
Sources
Primary: John Calvin, Institutes of the Christian Religion (1559), book 3.; Jacob Arminius, Declaration of Sentiments (1608).; Canons of Dort (1619)..
Secondary: Richard Watson, Theological Institutes (1826-1829).; John Wesley, Serious Thoughts upon the Perseverance of the Saints (1751)..