What's the advantage of using bra-ket notation over inner-product notation?

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Both notations look pretty similar, and appear similar when undergo algebraic operations. Apart from personal taste (aesthetics) concerning commas ($\langle \phantom{\cdot},\phantom{\cdot} \rangle$) vs. pipes ($\langle \phantom{\cdot}\mid \phantom{\cdot}\rangle$), what is (are) the practical advantage(s) of using the bra-ket notation over the inner-product notation?