Free of any influence from IVs, EVs, natures, items or any stat changes, Flamethrower is more powerful than Flame Wheel, 100% of the time. This is based on mere base stats and move power alone, though, so others factors like EVs and others previously mentioned may also play a role in determining which is more powerful. But going off of the baseline numbers that apply in all scenarios, Flamethrower is decisively better.
To find out this answer, I simply threw in a blank Rapidash set into Pokemon Showdown's damage calculator and matched it against a blank Arceus, a Pokemon with identical Defence and Speical Defence. The calculator, assuming both Pokemon are level 100 and both have the same set of perfect IVs, says that Flamethrower wins by a minimum of 0.6% and a maximum of 6.6% of Arceus' health.
0 SpA Rapidash Flamethrower vs. 0 HP / 0 SpD Arceus: 69-82 (18.1 - 21.5%) -- possible 5HKO
0 Atk Rapidash Flame Wheel vs. 0 HP / 0 Def Arceus: 57-67 (14.9 - 17.5%) -- possible 6HKO
With that being said though, Rapidash is still better as a physical attacker, as it has a reliable STAB attack in Flare Blitz and access to helpful coverage moves like Wild Charge, Megahorn and Drill Run. Its special side isn't nearly as fortunate, Solar Beam and Hidden Power being its best coverage options, and of course with the lower base stat.