The truth is the many people have a strong point of view here. And in my experience the answer depends on where we are from, in an industry and experience sense.
From the perspective of an organization Ability is a more tangible thing to build. We need to execute a set of initiatives in the coming years, which need certain capabilities, which stem from certain competence and so on - clear. Agility is more vaguely defined. It's more talked about in a relative sense, or in a 'I know it when I see it' sense. For many organizations, it's about cross-skilling the employees, which mostly means a policy of job rotations, and a capability view of the employee superseding the experience view.
One thing is clear to me - agility follows ability. I have seen organizations where job rotations happen annually. The head of the company is there by virtue of being the head of marketing before, and he got there because he was head of a different function before. The number three person in sales used to be a number three person in service. While these people have great cross-functional understanding, they sometimes do not get enough time to build functional expertise. The other extreme, is the much cited organization where people super-specialize and finally know everything about nothing - so much so that employees can't speak each-others' language.
What is the best approach depends a bit on the industry and the competition too. In a startup environment in a budding industry, one maybe needs to build a team that knows something about everything. If on the other hand you're competing in a mature industry at the efficiency game, then you need functional and domain specialization.
Finally, to re-emphasize, I'm not against job-rotations or the culture of building for agility - just that each layer in the pudding takes time to set. If we're replanting our plants very often, they don't grow so well, if they grow at all.
