My first was a 4th degree according to my doctor, my friends doctor called it a 5th degree. Mine went all the way through to my rectum.
My second was a partial 3rd. Can't remember my third. Fourth was very small tear, first one with a midwife. The last two I finally had at home and had no tearing at all.
I am awaiting the arrival of #7 any day/moment now!
My friend was told the same thing as you and she opted for a c-section.
Everyone's body is different, I have had good experience; use what you learn, pray about it, and make decision with your husband. I hope all goes well and you can have a satisfying birth.