The optimal competitive set would have both Eruption and Flamethrower. This way you can use a Fire type STAB even when you are low on health. Sunny Day is not a good move for Typhlosion in competitive, rather you should get some other Pokemon such as Uxie to set it up if you want to use it.
As for ingame use, Flamethrower is the better option, due to its reliability and higher PP.