It has to do neither with Anakin's power or anything else.
Dark Side of the Force destroys who you are. It eats you from within and punishes your actions. The more attuned to the Dark Side one is, the less powerful and attuned to the true nature of the Force you are.
When Vader let go of his anger, and turned to the Light, his natural connection to the Force strenghtened. I believe that Jedi strong enough in the true way of the Force (Light side) can manifest themselves easier, due to their connection and purity of spirit.