Class inheritance or Containers?

While talking with Daniel and Lorenzo about "Tree Reincarnated" I regularly stumble across the question what approach to use to implement different backends: "Class inheritance or Containers?".

I personally feel that using the container approach leads to massive code duplication, while using class inheritance avoids the most (most, because there's no real multiple class inheritance in PHP).

Container

<?php

class PublicAPI
{
    var $container; // !SpecificAPI

    function doSomething()
    {
        return $this->container->doSomething();
    }
}
?>

Class Inheritance

<?php

class SpecificAPI extends PublicAPI
{
    function doSomething()
    {
        // do something only this class needs to do
    }
}
?>

So what do you feel about this topic and how you'd handle that?

UPDATE

While looking again at Daniel's nice diagram, I feel like we've already reached the point where solving this problem with class inheritence is impossible (despite using aggregate*() - you're right Lorenzo, again :) have nice holidays! ).

Tree_Admin_Simple_MDB2 would have to extend Tree_Simple_MDB2 and Tree_Admin_Simple_RDBMS...

Mike's arrived at the dead end, again ;)