Nature of Enlightenment
You're absolutely right that they are only superficially appearing similar, but when you dive deep, they are completely different.
This has been discussed in numerous answers, which I will not repeat here - this answer, this answer, this answer, this answer, this answer.
The original teachings of the Buddha are systematic (the four noble truths), empirical (the three marks of existence), soteriological (the Noble Eightfold Path) and avoids intellectual gymnastics and obscure mysticism (Parable of the Poisoned Arrow, Acintita Sutta, Sabba Sutta), while Advaita is metaphysical and based on logic, philosophy and intellectual gymnastics.
For e.g. the Eternal Self as the Universal Consciousness or Cosmic Consciousness that is standalone, indivisible, eternal and witnesses through all living beings is a very elegant idea in Advaita Vedanta.
But the Buddha's empirical observation and realization is that consciousness is dependently originated on the six sensory media, and it is conditioned and impermanent (see MN 38). Even the mental idea of the self is also dependently originated, conditioned and impermanent. This can be realized generally through the Noble Eightfold Path, and specifically through vipassana.
So, which is true? If you dive deeper, you can see for yourself which is true. One is a very elegant intellectual model, while the other is empirically verifiable.