Is being a farmer more dangerous then being a firefighter?

No. Farming may be a dangerous profession at times, but any emergency personnel (Firefighters, Police Officers, EMT's, Paramedics, etc.) see danger on a more common basis.

There is nothing more dangerous than risking being shot, being exposed to any kind of disease, running out of air in a burning structure, having a burning structure collapse while inside of it, and countless other risks that all emergency workers may come across.