It's a huge change; that's for sure. I think it might be too much, because it will really hurt non-ToB melee characters, and they're the ones who need the most help. As far as feats go, I think it's decent, power level wise. I think it's a solid choice. I'd choose this in a game where regular PA wasn't available, but it changes so many things that are keyed on Power Attack (Leap Attack, Shock Trooper, etc) and that gets rid of a huge percentage of damage for melee characters.
On a semi-related note, I had a similar idea for a version of Power Attack that had no penalties, but this would be for an entirely different game. The idea is all classes would have abilities powered off of points (similar to psionics), and Power Attack could be something like +1d6 damage with an "augment" of +1d6 per additional point spent. Although that's for a different idea...
I rushed that one, as my internet access was being shut down for the night, so I didn't have time to finish explaining my stance on the idea. In terms of actual damage, this does more than the normal PA. The average (and optimal) use of PA only applies between a -3 through -5 penalty to attack rolls, then multiplies that until it becomes somewhere around 200 points of damage per hit. This removes the penalty, but sets the damage to a much slower scale (the character's Con mod). In doing so, it retains power at every level (the lower levels it's an extra 3-5 points of damage per hit, at the high levels you are effectively getting PA for 10 with no penalty to the attack roll, which ups the damage dramatically thanks to all of the multipliers). It does eliminate Shock Trooper and similar feats related to the penalty, but effects that multiple the damage from PA should be translated to fit the new version (multiplying your Con mod instead of the penalty).
The exception is 2-handed weapons. I left that part of Power Attack out on purpose last night. Without that change, One-Handed weapons aren't automatically out-classed by Two-Handed ones. Two-Handers still have the extra Str to damage rolls, but that's it now. Effects like Power Attack and the effects that multiply the extra damage no longer grant extra benefits for using a Two-Handed weapon.
Instead of the normal benefits of Leap Attack (100% increase for PA on a Charge, or 200% for using a 2HW), you get the latter of the benefits for any weapon you could PA with (any non-light weapon).
This also makes PA useful for TWFers, as the extra damage no longer comes out of your To-Hit modifier (which we all know is low for damn near everyone who isn't focused on it). The damage now comes from a stat you normally boost anyway (Con). In effect, while this does make MAD more noticeable, it pays off by rewarding you for making a tougher melee character.
Let me revise the feat idea. I'll remove the Str requirement, and make a few more changes.
[spoiler]Power Attack
You know how to shift your weight into each attack, adding more mass to the blow and putting more pressure on their defenses with each successful attack.
Prerequisites: Con 13, Proficient with a one-handed or two-handed melee weapon.
Benefit: Whenever you deal damage with a one-handed or two-handed melee weapon, you may add your Constitution modifier to the damage roll in addition to your Strength modifier.
Special: You cannot use this feat in conjunction with Weapon Finesse, or with weapons that allow Weapon Finesse (such as the Spiked Chain or Rapier).
Combat Expertise
Sometimes, the best defense is to just pay attention to where the enemy is swinging, and meet them half-way.Prerequisites: Int 13
Benefits: You can Fight Defensively without penalty as a Swift action. In addition, whenever you fight defensively or wield a shield you may add your Int modifier as a Dodge bonus to your AC (or the normal +2 for fighting defensively, if it is better than your Int modifier).
Normal: Fighting defensively is a Standard action (or Full round action) that applies a -4 penalty to your attack rolls for that round. Shields do not grant a doge bonus to your AC.
Weapon Finesse
You have mastered the art of fencing, and can show this competence with frightening efficiency.Prerequisites: Dex 13, proficient with a Light melee weapon or a weapon that can be used with Weapon Finesse (such as the Rapier or Spiked Chain).
Benefit: When attacking with a Light melee weapon or a melee weapon that can be used with Weapon Finesse, you may add your Dex modifier to the attack rolls instead of your Str modifier.
Special: You cannot use the Power Attack feat on weapons that benefit from Weapon Finesse.[/spoiler]
Ok, so all I really did is make the feats somewhat better and nerfed the Spiked Chain (because we all know it needs a kick in the nuts). The only real change to Weapon Finesse is the requirements. The change to Combat expertise is major, but increases MAD (somewhat). Warblades will love that and PA now.