First of all...when it comes to motivating your players, I've noticed that the old school managers do a great job. Torre, as much as I hated his in-game management, was probably the best I've ever seen.
However, I think the in-game management is the most important factor. If you need further proof, look at Grady Little.
Championships are a bit of a crock. If Girardi wins a World Series or two, does he suddenly become a great manager? I thought he was a good manager when he was with the Marlins. He's a good manager now, and he was a good manager then. I never thought Tito was a great manager, he was just better than Torre.
To me, a manager's job is 95% bullpen management and in-game strategizing. How many calls does an AL manager make during the game that doesn't involve pitching? Bunting or stealing? Come on...at most 2 or 3 times a game, if that. However, he has to know when to take the pitcher out, which reliever, etc.
Not only that, but he has to manage them over the course of the season. No one in the game does it as well as LaRussa in the NL, and although I am biased here a bit by my fandom, no one in the AL does it as good as Girardi in the AL.
Tito? Get real.
Francona's moves are baffling, to be honest. I can't understand what the heck he is doing in innings 6, 7, and 8. The 9th goes to Papelbon, but the rest is confusing. In that regard, he's very similar to Torre.
In comparing him to LaRussa, there should be no question. LaRussa has won everywhere he has gone. Whether you agree with "creeping LaRussa-ism", the fact remains that his technique has changed the game. He's an innovator, and one of the old guard who uses modern systems and analysis to maximize his moves.
In that regard, and for that reason, there is a huge gulf between LaRussa and managers like Tito or Torre. They can't hold their own against a LaRussa.