Most present day "evangelical Arminians" affirm eternal security, whereas both Arminius and John Wesley (who considered himself to be following in Arminius' footsteps) believed a Christian could fall from grace.
On the other hand, Arminius and Wesley were both strong on original sin. Wesley's famous sermon on Original Sin argues that it is literally impossible for an unregenerate man to perform a morally righteous act without God's grace as a help.
I would guess that most present-day evangelical Arminians would not deny, but would at least downplay, the effect of original sin on a person's behaviour.