A passing comment has led me to this conclusion: the ability to make decisions is often distinct from the ability to execute.
"Ability" here is meant primarily in organizational rather than personal terms. While some individuals may have a preference one way or another, the situation they find themselves in seems to influence their ability to do both simultaneously. In a reasonably contained organization, eg a small business, the chief executive needs to be able to make decisions and execute on them; there isn't an alternative.
As organizational complexity increases, executives are increasingly channeled into one modality vs. another. Some leaders make the hard trade-offs that lead to a vision and strategy. Others are more focused on execution; though such work in itself requires endless hard decisions to be taken, I distinguish those from the strategic decisions that shape an organization's future.