Arcanine over Rapidash.
Not because Arcanine is my favorite Pokemon. I'll give you reasons:
Arcanine has a Total Base of 555, it's honorable. It is outclassing starter Pokemon and some of the best Pokemon overall like Magnezone. 555 is high.
Rapidash has a Total Base of 500. It's not bad, it's just overpowered. It was good, before that Arcanine came.
Arcanine's Abilities are Intimidate, Flash Fire and Justified. The first is useful; if somebody planes to Bulk up, he will have to do twice to receive an attack boot. The second has its use ; You can switch Ferrothorn facing another Arcanine to take the hit and receive nothing but boost in Fire Attacks. Finally, the last one can work but seldom. You can use it in double with Beat Up Weavile at your side so that Arcanine takes damage and boosts attack, while Lucario do the job better, Cobalion can even.
Rapidash's Abilities are Flash Fire, Run Away and Flame Body. The first one is the one you will always use, for the same purpose as Arcanine but in a much weaker situation. The second is competitively useless as it has no effect in-battle, just to let you run away from wild Pokemon. It cannot be used, as Rapidash has enough speed to outspeed wild Pokemon. The Last one is not much used, because Rapidash's bulk, 65 HP / 70 DEF / 80 sp.DEF is a joke ; Rapidash cannot take a physical hit in a competitive battle before to die. OK I know you want this for LeafGreen and FireRed, I'm giving advices in every place. In any fact, take Arcanine.
Arcanine's offensives are 110 ATK / 100 sp.ATK, making it able to use both physical and special attacks easily. Its movepool is a complement to this.
Rapidash's offensive are 100 ATK / 80 sp.ATK, which is seriously weaker. Arcanine is capable of much more than Rapidash.
Arcanine's bulk is nice ; 90 HP / 80 DEF / 80 sp.DEF, which outclasses by far other Fire Pokemon that has its purpose.
Rapidash's bulk is a vast joke compared to Arcanine : 65 HP / 70 DEF / 80 sp.DEF. Ridiculous.
Arcanine's speed is 95. It's good, but if it was higher, Arcanine could be easily OU.
Rapidash's speed is 105. It's the only point where it outclasses Arcanine. But 10 points ? OK, Arcanine @ Scarf become quicker. Rapidash, since what I know, never plays Scarf. It's usually Sash, so it can attack once more. Never mind ^^
The movepool that Arcanine could use in Gen I is bad compared to today, but Rapidash's is not better.
Arcanine can use:
EV: 52 ATK / 200 sp.ATK / 252 Spe
- Double Edge
- Hyper Beam
Limit, these are strong moves, while in Gen I, I ain't sure there was better.
Rapidash can use:
Trait: Flash Fire
EV: 252 ATK / 252 Spe / 4 HP
- Fire Blast
- Horn Drill
- Double Edge
And I think that's it. Arcanine is largely better. For Gen I.
For Gen V, you can check the asked questions or my wall post ;)