On the outside. Remember it is intended to deter something from digging in. It's not necessary to bury it deep. Mine is somewhere between 1 and 2 inches. I have a friend in a rural area who didnt even bury his, just let it lie (lay?) on the ground, then let the local vegetation grow up through it.
One thing I realized this year.....If you plan on planting anything in the ground (grapes, other vines or stuff) plan on it and cut some openings into it before you lay down the wire, and bury it. I have spent lots of time this year unburying wire, and cutting openings in it that will allow me to plant some grape vines so that they will grow up my fence to provide shade for the girls.