Answer:
Doctor
Step-by-step explanation:
Although both are equally important, (Farmer's preventing mass starvation and doctor's treating ailments) I'd have to go with doctors. If, for whatever reason, we ended up going through a mass starvation... we'd still have multiple food options. Artificial food and stock from neighboring countries. If we'd lose doctors it'd basically be genocide. Most people wouldn't know what to do if they broke their arm or developed a fatal heart disease. They're not qualified to treat such conditions and could end up making the condition worse if they attempt to do so.