Not much different. I've got a dim impression as usual. ^^ '집에 가다가' is focused on 'home' and the action of 'going' directly, whereas '집에 가는 길에' implies that the person's mind is open to the scenes and possible events on the way home. Well, can I say, target-focused versus process-focused? I am afraid it is not helpful. I said it was my impression, very dim and faint.