I agree that they're basically the same thing.
I would honestly prefer it if they didn't add pure damage at all to any ability or weapon, and had more general effects. I disagree with your choice of benefits for the following reasons, though:
Strength giving critical hit damage would make strength the preferred attribute for daggers because of Backstab.
Finesse having a chance to give free AP makes combat extremely random.
Intelligence giving cooldown reduction would cause it to have breakpoints for individual skill cooldowns "3 turn cooldowns are reduced to 2 at XX Int, and to 1 at XX Int." Etc.
It's pretty hard to balance this properly and making each statistic a valuable choice for their respective archetype, like finesse is for rogues, and Intelligence for wizards. (Critical hit damage to finesse, and cooldown to Intellgence get fairly close, though, as far as examples go)
