Well... I actually wrote a story called The Cricket and the Snail, which is going to be published by Guardian Angel Publishing soon. Same sort of idea, in that patience and perseverance prove more important than speed.
I think I would change it from winning a race to completing an important task - the one who does it fast without real thought. just to be the first done, does so poorly and it falls apart - the one who takes the time to do the task properly has something that lasts and ultimately "wins".
I would add a rematch in which the hare does not repeat his mistake and wins like he is expected to. The tortoise should finish the race anyway; and, he should point out that the only person you really need to compete against is yourself. Honestly, a lesson about how to handle second place would have been more useful to me growing up than "I could win a race because of someone else's over confidence."
I also find that the phrase "slow and steady wins the race" is not used in the working world, judging by peoples' actions.