What are the basic differences between Calvinist theology and Methodist theology?

This question reaches further than any one document or answer can touch upon. There is simply too much history between the two schools of thought to formulate an unbiased answer, and if the truth were to be known, both schools are as divided inwardly as they are between one another. Any “Methodist” theology (assuming the presupposition that John Wesley is the seat of this theology) must take into account that the Wesley’s presuppose Calvinist theology (among many others) and Calvinist theology presupposes the great theologians that came before John Calvin (Augustine, for example, on which much of Calvinism is based). Remember, John Calvin lived some 200 years before John Wesley. We also must realize that any theology is based on the human attempt to understand God’s logic (theology, by definition), and that it is safe to assume that any theological doctrine, therefore, is flawed and more than one theological stance may be correct (as long as they don’t contradict) or a combination of doctrines is probably more accurate (because no human has the fullness of truth).

That being said, the “TULIP” formula may be the best known summation underscoring the differences in the two schools of thought (though neither school is limited to the five points of the formula). Calvinism is, then, summed thusly:

‘T’ – Total Depravity – humanity is totally depraved and, not just unwilling, but unable to seek God without the illumination of God’s grace.
‘U’ – Unconditional Election – God unconditionally elected some to salvation, while others were, not passively, but intentionally elected to reprobation (damnation).
‘L’ – Limited Atonement – the atoning work of Christ on the cross was effectual only for those unconditionally elected for salvation by God.
‘I’ – Irresistible Grace – the one that was unconditionally elected for salvation cannot say “no” to the Holy Spirit’s application of Christ’s atonement.
‘P’ – Perseverance of the Saints – those unconditionally elected to salvation are preserved by God and can never lose their salvation.

Methodist theology, concerning TULIP, says:

‘T’ – Total Depravity – Wesley rejected the idea (preferring “complete corruption”) until later in his ministry, when he accepted the thought of humanity’s complete rejection of God without Christ.
‘U’ – Unconditional Election – Wesley and most Methodists reject this premise outright. They believe that Christ died for “all” and He “does not wish that any would perish.”
‘L’ – Limited Atonement – Wesley and most Methodists believe in “unlimited atonement.” Not that Christ brought about universal salvation, but that all sins of all humanity have been atoned for by Christ.
‘I’ – Irresistible Grace – Wesley and most Methodists believe in “resistible grace.” Humanity can reject God’s grace simply by acting out of their total depravity (or complete corruption).
‘P’ – Perseverance of the Saints – Wesley and many Methodists believe that a believer saved by grace can sin to such an extent that that one can lose their salvation.

Personally, I agree with the Calvinist view on the “Total Depravity” of humanity because of the sin of Adam.

Augustine of Hippo once explained it like this:
In the garden, before the fall, humanity was able not to sin.
After the fall humanity is not able not to sin.
In heaven humanity will not be able to sin.

I also agree with the Calvinist view on the “Perseverance of the Saints” (for the reasons I explained in ‘Can you lose your Salvation?’ on my blog).

I agree with the Methodists (with qualifications) concerning the other three points. In my opinion, Christ died for all as the Scriptures explain. Christ’s atonement is “sufficient” for all, but “efficient” only for those who believe (this point was actually formulated by a Calvinist who wished to better align doctrine with the other founding Reformers – Luther and Zwingli). And I agree that God’s grace is resistible (based on other Wesleyan premises, which are beyond the scope of this essay. I will cover these in a later answer) because of the human “freedom of choice” (similar to “free will,” which term I do not hold dear for reasons beyond this essay).

Again, I think that both forms of theology are extremely helpful, and no one school of thought is complete without the other. The idea of balance is the wisest choice when it comes to any belief-system or thought because it, in and of itself, reaches the goal of making one think about the logic of God (theologize).