I've likewise thought of something similar in nature to what Roudi is suggesting, but I also had another category added (this was before d20 Modern, so bear with me): Karma, which was divided into two sub-sections: Luck and Experience.

Luck allowed you to affect the outcome of a single circumstance through the use of Hero Points (think of over-powered Action Points).  The amount you "generated" per session was based off your score.

Experience allowed you to increase the amount of experience you gained (or lost) each time you gained generic experience (taken from various video games).  However, this quickly lead to becoming a "must-have" stat.  I was in the process of rewritting this, when I discovered a new mistress - d20 Modern.  

Anyway, I didn't run it based on the modifiers - rather on the sum of the score (i.e. if you had a 14 in Intelligence, you could break it down by any amount between the two sub-sections, so long as the sum equaled 14).  While I can understand the desire to do this (it came about as a result from someone who wanted to be really good at ranged attacks, but not defense - don't ask), I'm not sure I ended up liking what I had came up with.

Roudi's idea makes more sense to me, just for the record, using the modifier as the "determining" factor.

Just my thoughts on the subject.  Also, for the record, I never played any other edition of D&D, and was unaware that this idea existed in any edition of it.  What was that book called again?

Peterson

This spliting of ability scores was done in AD&D 2nd Editon in the Players Option: Skills and Powers book.

Strength: Stamina, Muscle
Dexterity: Aim, Balance
Constitution: Health, Fitness
Intelligence: Reason, Knowledge
Wisdom: Intuition, Willpower
Charisma: Leadership, Appearance

Quote from: EmryysThis spliting of ability scores was done in AD&D 2nd Editon in the Players Option: Skills and Powers book.

And boy, was it open to abuse...

QuoteStrength: Stamina, Muscle

Stamina: Weight allowance.
Muscle: attack, damage, open doors, bend bars, max press.

QuoteDexterity: Aim, Balance

Somewhat balanced... Aim: Ranged attacks. Balance: AC, I think surprise.

QuoteConstitution: Health, Fitness

Health: System shock, Resurrection survival (I might be wrong on one of these).
Fitness: hp.

QuoteIntelligence: Reason, Knowledge

Reason: Some wizard-only stuff.
Knowledge: Some other wizard-only stuff and proficiencies.

QuoteWisdom: Intuition, Willpower

Intuition: Cleric spellcasting stuff.
Willpower: Saves vs. magic.

QuoteCharisma: Leadership, Appearance

Leadership: Henchmen stuff.
Appearance: Reaction modifier.

For many of these, it was sort of a no-brainer which one to increase at the expense of the other (Fitness, Knowledge, Willpower). Also, given the way you needed high stats in 2e to get any benefit, they were very easy to manipulate ("Oh, I rolled a 14 for Con. That's no extra hp, and system shock 88%. I guess I'll increase Fitness to 16 and drop Health to 12, for +2 hp and SS 80% instead.")

With Skills & Powers, I fiddled with the stats to get them a little more balanced (though there wasn't much one could do to balance Strength's subabilities) and I used the OD&D Rules Cyclopedia ability score bonuses (13-15 = +1, 16-17 = +2, 18-19 = +3, etc.).  In the end, it was still munchkiny but, more importantly, it didn't really add any fun to the game.  So when 3e came out, I happily dumped it.