Arminian
Man's depravity is only partial. Man is not left in totally helpless state. His will is not affected by sin. It is still free to choose good over evil, and could repent and believe. Faith is the sinner's contribution to his salvation. His eternal destiny depends on how he uses his free will.
Calvinist
Man is a free moral agent, and his will is in bondage to his nature. He cannot change his nature. He cannot make choices contrary to his nature. He is dead in his trespasses and sins and is drawn to the god of the dead.
Biblical Position
Man's natural fallen spiritual ability is limited. Men of flesh, i.e. not regenerated and thus spiritually separated from God, can understand the milk of the gospel (1 Corinthians 2:14-3:3) but not spiritual meat, which requires being indwelt with the Holy Spirit.
Arminian
Election is based upon God's foreknowledge, which means He looked down the corridors of time and saw who would believe the gospel, and so chose those who were willing to choose Him.
Calvinist
God saw that no one would believe on his own, so He chose some before the foundation of the world, according to His own pleasure and purpose, and gives them the faith to believe.
Biblical Position
Ephesians 1:4 says God chose us in Him before the foundation of the world. Both Calvinists and Arminians read "chose us individually in Him" into the text. However, in light of other scriptures i.e. 2 Thessalonians 2:13, which say God chose us through faith in the truth, Ephesians 1:4 must be understood to say God chose us in Him corporately before the foundation of the world. In other words, God chose the Word to be His Lamb, His Redeemer, and therefore in effect chose everyone subsequently redeemed by the Redeemer.
Arminian
Christ's death was "sufficient" for all but "efficient" only for the ones who would believe. It had unlimited purpose but a limited power (limited by man's free will). It did not in fact secure the salvation for anyone, it only made salvation possible.
Calvinist
The intention of Christ's redeeming work was to save the elect and in fact secured salvation for them. God has a limited purpose (save the elect) and an unlimited power. Christ secured the salvation of those for whom He died.
Biblical Position
Christ died for all mankind because God desires all men to be saved according to His purpose and plan. But no one receives the reconciliation provided by Christ's sacrifice unless God credits their faith as righteousness (Romans 4:5) and spiritually places them in Christ (1 Cor. 1:30). So Christ both provides reconciliation to all mankind and provides salvation for all those spiritually placed in Christ by God.
Arminian
God wants to save everybody, but inasmuch as man is free, he can resist God's will. The Holy Spirit can draw only those that allow Him to draw them. They first have to be willing to believe.
Calvinist
The external call given to the all who hear the gospel can be and often is rejected. The internal call made by the Spirit to the elect cannot be ultimately resisted. The Spirit graciously causes the elect sinner to believe, repent, and come willingly to Christ.
Biblical Position
God does desire all men to be saved but according to His purpose and plan which is to choose those whose faith He credits as righteousness. God's plan is not to compel faith via irresistible grace, but to be glorified by those who autonomously repent and trust in God. God grants repentance by providing the opportunity through His revelatory grace, i.e. the gospel of Christ, and by not prohibiting repentance by hardening, except in cases where the hardening is in according with His purpose, i.e. the unbelieving Jews of Romans 11.
Arminian
Believers who are truly saved can lose their salvation by failing to keep up their faith. As man's will is the instrument of his salvation, it can also be the instrument of his falling from grace. The Christian must persevere to the end or be lost. (Some who believe in the other points of Arminianism reject the idea of falling from grace and embrace eternal security.)
Calvinist
While the saint is preserved by God, true faith will persevere, even though it may stumble and fail. They will arise and go on in the faith. They are eternally saved.
Biblical Position
Once a person is spiritually placed in Christ, they are sealed in Him forever, so once a person is actually saved by God putting them spiritually in Christ, they are saved forever. God also protects their faith and devotion to Christ, 1 Peter 1:3-5, keeping them as in a locked cell, but He does not protect a person's ministry so we might build with perishable stuff and enter heaven as one escaping from a fire.