Great question and I went through it. I was nearly subjected to a Pauline BUT the priest and the Diocese decided that the annulment was SIMPLER and would take less time.
I was raised Catholic – BUT denied the sacraments due to my atheist father. Meaning I had the spiritual upbringing for the majority, yet I had not received the sacraments until after the first marriage was over and I was ready to fully participate in my own faith, read: my choice – in adulthood. I was not baptized nor practicing any faith when I first married. That marriage lasted about the length of a sneeze.
So although you were baptized, the fact that he wasn’t helps your case immensely, and if you have a witness who can say he wasn’t baptized, and not a practicing Christian in a RECOGNIZED Christian religion (meaning no LDS or JW’s) you should have your annulment granted easily enough. Each tribunal can be different in their demands of passing an annulment through. Even the cost of the annulment can vary from diocese to diocese.