"to vest" vs. "to invest (as a metaphor)"

While both usages are correct, they express different ideas. Vested is not a substitute for invested, despite the similarity in the words.

To be invested in something means that one is devoting resources such as time or energy to its success -- whether it's an organization, a scheme, a business venture, and so on. So the first sentence means

"If we give lower-level people more decision-making power, they will feel like they have a bigger stake in our organization."

To be vested means that you're protected by law, commitment, or some other social institution. A vested thing is a strongly-held thing that's difficult to take away. So the second sentence means

"If we give lower-level people more decision-making power, they'll be more motivated to do a good job since it's difficult to take away that power. They'll be able to act more directly to help our organization succeed."

Here, the thing that's protecting the power and which makes it vested is a presumption: namely, that giving the lower-ranking people more decision-making authority is a decision which will not lightly be revoked.

Vested is a legal term. It means to have a right of ownership that is not conditional. For example, after you have paid your mortgage, you have a vested ownership in your house. The mortgagee (bank) can no longer foreclose.

Unless the shareholders of the corporation are all employees of the corporation as well, the term vested does not fit. Employees with decision-making power would be invested in making the corporation run well, but without ownership, they would not have any final authority. Their powers are not vested.

from Law Dictionary Online: "vested adj. Referring to having an absolute right or title, when previously the holder of the right or title only had an expectation. Example: after 20 years of employment Larry Loyal's pension rights are now vested."

In your example, you are using vested incorrectly: "...enables the individual to feel more vested in the overall success..." There is no more or less vested. The right is vested or it is not vested: binary. It could be not yet vested (an expectancy or contingency) or divested (once vested; now sold, traded, or lost). Also, since the status of vesting is a verifiable fact rather than a subjective state of mind, "to feel vested" makes no more sense than "to think hungry."

If you don't like "invested" for your purpose, you could use "to feel involved", "to have pride of ownership", "to share the achievement" or the colloquial "to have skin in the game".