How is it different from advaita and vishistadvaita, and how does it reconcile yoga and Sankhya with vedanta?
These questions are perfectly explained by Surendranath Dasgupta in his “History of Indian Philosophy”, 3rd volume, chapter 22 named “The Philosophy of Vijñāna Bhikṣu”
How is it different from advaita and vishistadvaita
This is a very broad question, but here are some key concepts regarding Vijñāna Bhikṣu’s philosophy known as Avibhāgādvaita (‘non-duality of non-separateness’), implemented in his Vijñānāmṛta-bhāṣya: his commentary on the Brahma-sūtras.
The production, existence, maintenance, modification, decay and destruction of the world are from Brahman as God. He holds within Himself all the energies constituting the prakṛti and puruṣas, and manifests Himself in other diverse forms; Brahman as pure consciousness is associated with the conditioning factor of His own being, the māyā as pure sattva quality in all this creative activity, so from that great Being who is devoid of all afflictions, karmas and their fruits are also produced.
How does it reconcile yoga and Sankhya with vedanta?
Bhikṣu thinks that the Sāṃkhya and Yoga philosophies are intimately connected with the Vedānta and are referred to in the Upaniṣads. For this reason when certain topics, as for example the problem of experiential knowledge, are not described in the Vedānta, these are to be supplemented from the Sāṃkhya and Yoga. If there is any seeming antagonism between the two, these also have to be so explained that the opposition may be reconciled.