All-Star Teams and the Fallacy of Composition

After the baseball all-star game, I started thinking about critical thinking. I use all-star teams as an example of the fallacy of composition which is the flawed argument that what is true of the parts must also be true of the whole. It is true that the all-star team in any sport has the best player at each position, but this does not necessarily mean that while the players making up the team are the best, that the team itself is also the best. You could have a line-up of prima donnas who do not have the right chemistry and all expect to be the star.

But while the whole does not necessarily partake of the properties of the parts, it could. So, given a choice between the championship team and the all-star team, which should one pick or in which cases would you select one or the other?