What's the difference?

I've been thinking a lot over the last week or so about being stubborn and being persistent.  I got as far yesterday as looking up definitions for these 2 words and really, on paper, they are more similar than one might think.  The difference seems to be mostly in connotation.  If I hear someone say a person is stubborn, the image that comes to my mind is an inflexible attitude and an uncooperative spirit.  However, if a person is described as persistent, I would see someone who keeps at their task, whether chosen or assigned, until it's completed.

When it comes to a life of faith, is one word better than the other?  Does each word have pros and cons?  Can someone be stubborn and persistent about the same thing?  As always, my readers, your comments are welcomed.