It really depends on whether your Pokémon is Physical or Special. But if your Pokémon is mixed... let's view some pros and cons.
Flare Blitz
Info: 120 Base Power, 100 Accuracy, 15 PP. 1/3 recoil damage, with a 10% chance to burn. Also, if the user is frozen, Flare Blitz thaws out the user.
Inferno Overdrive Base Power: 190 Base Power
Pros:
High base power!
100 Accuracy.
Okay PP.
10% chance to burn!
Thaw before attacking.
Cons:
1/3 recoil.
Lower Inferno Overdrive Base Power compared to Overheat.
Flare Blitz Summary: All though the 1/3 recoil is what greatly hinders Flare Blitz, when used with proper healing Flare Blitz can be extremely powerful and spam-able.
Overheat
Info: 130 Base Power, 90 Accuracy, 5 PP, lowers user's Special Attack two stages after attacking.
Inferno Overdrive Base Power: 195 Base Power
Pros:
High base power!
Okay accuracy...
Higher Inferno Overdrive Base Power compared to Flare Blitz!
Cons:
Low PP (5)
Stat drop
90 Accuracy sometimes does not cut it.
Overheat Summary: Despite having high power, the stat drop is why people may not choose Overheat as much. In addition, you might not even get any damage off with 90 accuracy. Switching out to get rid of stat drops can sometimes be very predictable.
Overall Summary: If you have a Physical Attacker, use Flare Blitz. If you have a Special Attacker, use Overheat. If you have mixed, I would probably choose Flare Blitz over Overheat. Mostly only choose Flare Blitz if you have healing options on your team. Flare Blitz can definitely work without healing, however. Stat drops and 90 accuracy for Overheat are the main reasons to pick Flare Blitz over Overheat when you have a mixed attacker.