Arminian Free Will ---all boils down to us "accepting" the free gift. It seems that many arminians will wholeheartedly agree that the Holy Spirit draws, that God is very involved in the process of a non-christian learning the Gospel, but will stop short of accepting that this drawing is irresistible It seems that they believe that God gives us the ability to make the choice, but we could still decide against Him. It's like they can't bear to think the God would actually make us WANT Him--There's that little part inside that says "NO I want to make that final decision! I want a little piece of the Glory!" They just can't accept that once God opens your eyes, you cannot resist Him, and why would you want to?
Calvinist Free will---accepts that, as Jon so well put it, our will is contingent. We will make choices based on what we most strongly desire at any given moment, and when God opens our eyes and hearts, we most certainly desire Him above all. Until that moment, we don't see spiritually, or understand spiritually, so how could we possible make a free will choice for Him when we don't even have that option? It's just not there. We are ignorant of God.
Our "will" is so much more free when we are in Christ. Because we finally have the ability to make a choice for God, and our good deeds are finally pleasing to Him because we make them for the Glory of God and not for our own gain or glory.