Is the word estante the same in Brazilian and European Portuguese?

Yes

The word "estante" has the same meaning, spelling, and grammatical gender in both Brazilian and Continental Portuguese. The only difference is pronunciation.

In Brazilian Portuguese, the vowels are generally more open and the unstressed "e" is clearly articulated (sounding like es-TAN-chee). In Continental Portuguese, unstressed vowels are often reduced or even suppressed, making the word sound much more closed and clipped (sounding more like sh-TAN-t).

Brazilian Portuguese Examples

1. Comprei uma estante nova para o meu quarto. (I bought a new bookcase for my room.)
2. Coloca os livros na estante, por favor. (Put the books on the shelf, please.)
3. Essa estante de madeira quebrou ontem. (That wooden bookcase broke yesterday.)
4. A estante está muito cheia de coisas. (The shelf is very full of things.)
5. Eu preciso arrumar a minha estante. (I need to tidy up my bookcase.)

Continental Portuguese Examples

1. Comprei uma estante nova para o meu quarto. (I bought a new bookcase for my room.)
2. Põe os livros na estante, por favor. (Put the books on the shelf, please.)
3. Essa estante de madeira partiu-se ontem. (That wooden bookcase broke yesterday.)
4. A estante está muito cheia de coisas. (The shelf is very full of things.)
5. Eu preciso de arrumar a minha estante. (I need to tidy up my bookcase.)