Arminians hold to the 5-points of the Remonstrant. These 5-points states:
The Protestant TULIP, which was developed in response to the Arminian Remonstrant, believes:
It's a muddled mess.
Link: What is Arminianism?
Yes, the stuff in green looks like a fair summation of the Catholic theology of predestination.
It, of course, leaves our Arminian Protestant friends much room for error in other areas where they stray from the Church, such as necessity of the Holy Tradition, necessity of sacraments of the Church, necessity of charitable work, infused grace, veneration of Mary and saints, the papacy, and purgatory. Anything I forgot?
First of all, unlike Arminianism, we do believe in Predestination! We believe that the Elect are irresistibly led by God (if one would look back on their life, they would see God's effect. We can't see it very well from our point of view since we can't see into the future).
For example, "God, by His eternal resolve of Will, has predestined certain men to eternal blessedness". DE FIDE!
"God, by an eternal resolve of His Will, predestines certain men, on account of their foreseen sins (a bit different then the first one), to eternal rejection" DE FIDE!
As you probably know, St. Augustine defended predestination against the Semi-Pelagians who thought one could come to God after Baptism without grace. Predestination is a part of the Divine Plan of Providence.
The big "problem", however, is whether God has taken the Predestination of the Elect with or without the consideration of the merits of the man. Many early Catholics would say "no", such as St. Augustine and St. Aquinas. However, more recent Catholic theologians would say God MUST take it into account, as God sees everything as one "NOW", thus, makes decisions "simultaneously" with out actions in time. This is an open question in Catholicism and one can hold either point of view - as I have said before. This appears to be a difference between us and Arminianism. Of course, we do not believe that God predestines the reprobate, which Calvin taught. Thus, I say that Catholics fall in between the two extremes of Calvinism and Arminianism.
With this said, thus, Catholics would see that #1 and #2 could be potential sticking points with the Remonstrants. Number one has the potential to turn to Semi-Pelagianism, and #2 suggests that God MUST consider our merits when determining His elect - we do not teach either point infallibly. I would say 3, 4 and 5 are pretty much in line with our beliefs. However, with TULIP, 2, 4 and 5 are pretty close, 3 we can reword to say "efficacious" graces save but not sufficient graces. Number one, we'd reword that one to say "inability to choose God alone without His help".
My knowledge of Protestantism seems to be stuck in classical Protestantism, and I admit that I need to do some more reading to when Protestantism split between the two schools noted above. I have purchased the 5 volume set of Pelikan's The Christian Tradition, A history of the Development of Doctrine, and have read the 4 books - but not the last one, which covers from 1700 to now. Maybe I should read it? But I should know better, as the 4th book does cover the Remonstrants and the Reformed Theology, as well as toucing on the Anabaptists.
Sorry, there is already enough to know as a Catholic, with Scripture, Tradition, the Fathers, the Catechism, the Liturgy and Sacraments, and 2000 years of history!
Regards