The practice of meditation is central to certain Buddhist traditions, e.g. Vajrayana, Dzogchen, Zen, important for recognizing Buddha nature.
Furthermore, Vajrayana and Theravada traditions assert that the meditation serves as a basis for realizing selflessness:
the purpose of meditative stabilization is to serve as a basis for achieving supramundane special insight realizing selflessness, the emptiness of inherent existence, through which afflictive emotions can be removed completely and forever
-- Dalai Lama
So what is the purpose of satipaṭṭhāna? The purpose is to see anattā, that there is no self, no me, nor anything that belongs to a self.
-- Ajahn Brahm
And even highly accomplished Buddhist meditators have found that with a radiant mind in meditation, the sense of self can still fail to be uprooted.
At that stage the mind was so radiant that I came to marvel at its radiance...
“If there is a point or a center of the knower anywhere, that is an agent of birth.”
How exactly does Buddhist meditation practice lead to realizing selflessness, versus other forms other forms of meditation which do not? What exactly makes Buddhist meditation different?
What made the Buddha's meditation technique differ from others' (e.g. Alara Kalama and Uddaka Ramaputta) which did not lead to enlightenment? (Please be more specific than "Middle Way").