In the Buddhist Pali text, there is a dialogue between King Prasenjit and his wife Mallikā, that is remarkably similar to the Yajñavalkya-Maitreyī dialogue in the Bṛhadārṇayaka Upaniṣad. So similar are these two dialogues that it is likely that Upaniṣad was the source for the Pali text. Yet, despite the similarity, there is a twist at the end which separates the teaching of Bṛhadārṇayaka Upaniṣad from that of the Buddha. Here is the short dialogue from the Pali Buddhist text, Saṃyutta Nikāya (3.8):

At Sāvatthī. Now on that occasion King Pasenadi of Kosala had gone together with Queen Mallikā to the upper terrace of the palace. Then King Pasenadi of Kosala said to Queen Mallikā:

"Is there, Mallikā, anyone more dear to you than yourself?"

"There is no one, great king, more dear to me than myself. But is there anyone, great king, more dear to you than yourself?"

"For me too, Mallikā, there is no one more dear than myself."

Then King Pasenadi of Kosala descended from the palace and approached the Blessed One (Buddha). Having approached, he paid homage to the Blessed One, sat down to one side, and related to the Blessed One his conversation with Queen Mallikā. Then the Blessed One, having understood the meaning of this, on that occasion recited this verse:

"Having traversed all quarters with the mind, One finds none anywhere dearer than oneself. Likewise, each person holds himself most dear; Hence one who loves himself should not harm others."

Here both Prasenjit (in Pali: Pasenadi) and his wife Mallikā confess to each other that they love their own selves more than any other in the world. Read without context, it seems a rather strange assertion to make. Ideally, Mallikā should have said to the king, "You are dearer to me than myself" and King Prasenjit should have replied similarly, so that they would have strengthed their mutual love.¹ Instead, both of them said that their own selves are more dear to them.

This dialogue makes sense only when we assume that the Sutta writers knew, at least in parts, the Yajñavalkya-Maitreyī dialogue and wanted to fit that teaching in a Buddhist ethical context. Here is the Upaniṣad dialogue between the Sage Yajñavalkya and his wife, Maitreyī. Yajñavalkya says,  

One holds a husband dear, you see, not out of love for the husband; rather, it is out of love for oneself (atman) that one holds a husband dear. One holds a wife dear not out of love for the wife; rather, it is out of love for oneself that one holds a wife dear. One holds children dear not out of love for the children; rather, it is out of love for oneself that one holds children dear….. You see, Maitreyi—it is one's self (atman) which one should see and hear, and on which one should reflect and concentrate. For by seeing and hearing one's self, and by reflecting and concentrating on one's self, one gains the knowledge of this whole world..

For when there is a duality of some kind, then the one can smell the other, the one can see the other, the one can hear the other, the one can greet the other, the one can think of the other, and the one can perceive the other. When, however, the Whole has become one's very self (atman), then who is there for one to smell and by what means? Who is there for one to see and by what means?²

This famous teaching is purely ontological. At the level of ātman, the world is non-dual, so once you know that your ātman is the same as the entire reality, then you will treat the whole world as your own self. In that state of realization, husband, wife, children, friends, and everyone else are not separate entities but part of the fabric of the same underlying reality. Therefore, the love that we have for our fellow beings is not because they are different from us, but rather, they are part of our very ātman.   

However, in the Pali text, there is no teaching of ātman. Rather, the Buddha provides an ethical interpretation that love for oneself preclude one from harming others. Since each of us loves oneself the most, one should realize that it is true for others too and treat each other with love and respect.³ However, this sidesteps the issue involved that loving oneself the most in the world is rather selfish, and it is not always the case that one loves oneself the most; for instance, mothers usually love their child the most in the world.

On the contrary, the Bṛhadārṇayaka Upaniṣad is not teaching about the love of one's identity (the small 'I'), but the love of the ātman that is the underlying basis of our identity and a source of unity among all sentient beings. Holding oneself to be the dearest can only be an ethical doctrine based on the non-dual ātman ontology. It cannot possibly be interpreted ethically without the underlying ātman ontology, as Buddha has tried to do.

However, this is just our view, and other interpretation of both this important dialogue is welcome!