What often gets overlooked with Moyes is exactly how long he's held the manager's job at Everton. He's been at the club for a decade now, and thus has acquired an attribute of experience that few other modern managers possess; the experience of long-term development of a single club over many years, experience which we'll be losing when SAF retires.
Is Mourinho capable of taking over such a project with the expectation of continuation and longevity as the United managerial role? He may have bags of experience winning trophies with infinite cash at his disposal, but his experience at being dedicated towards a long term project is nil. Mourinho receives fair criticism for his lack of youth development, something which will always be the case as he has no experience whatsoever in working on a club from the ground up; he's a first XI man without any proficiency in managing other areas of a club, areas which Sir Alex has steadily built Manchester United around from the very beginning, to the extent that such long-term planning and grass-roots development represents the very essence of what is Manchester United.
What Moyes would bring with him is exactly that experience of long-term building of a club at every level, he's the same style of manager as Ferguson, and for me that's perhaps the single most desirable trait to look for in SAF's replacement; somebody who'll have the experience and ability to continue and expand on SAF's masterpiece, somebody who'll bring new ideas but nevertheless respect the ethos and philosophy in place already at the club, rather that than somebody who'll lay waste to the good work, ignore it completely in favour of a few magabucks signings before moving onto the next short-term project in four seasons' time.
Experience in the Champions League and the collection of silverware can be acquired, but the correct attitude in regards to long-term development of a club at every level is something which few modern managers will ever possess. Moyes has that.