It depend on case by case. both words meaning in english is prevention. but 예방 have more meaning. That is preparing about something in future. So if you know something when appear, then using 예방. but you don't know something when appear, but know it is possilbe appear, then using 방지. ex) 예방주사 : already know, when will be flu come. 과속 방지턱: We don't know when car has overspeed, but that make car can't has overspeed.

The focus is on that word 예. In fact both come from hanja and 예 does have a meaning in hanja. Its meaning is beforehand. So there go words such as 예약, 예정... So, in a nutshell, it has a further sense of doing something in advance as a protection.

I think,, it's just use that way. sorry... I'm never wondering about this.. you can use 사고예방 but can not use 감기방지