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

Yes

The only difference between "debaixo" in Brazilian Portuguese and Continental Portuguese is pronunciation. In Brazil, the pronunciation tends to be more "open," with clearly articulated vowels and a more syllabic rhythm. In Portugal, the pronunciation is more "closed" or reduced, meaning unstressed vowels are often shortened or swallowed, resulting in a more stress-timed rhythm. There are no differences in meaning, spelling, or the grammatical function of the word.

Brazilian Portuguese Examples

1. O gato está debaixo da mesa. (The cat is under the table.)
2. Eu deixei as chaves debaixo do tapete. (I left the keys under the rug.)
3. Ele não gosta de ficar debaixo do sol. (He doesn't like being under the sun.)
4. Tem algo debaixo do sofá. (There is something under the sofa.)
5. Ela se escondeu debaixo da coberta. (She hid under the blanket.)

Continental Portuguese Examples

1. O gato encontra-se debaixo da mesa. (The cat is under the table.)
2. Pusemos o livro debaixo da almofada. (We put the book under the cushion.)
3. A criança escondeu-se debaixo da cama. (The child hid under the bed.)
4. O objeto está sob o tapete. (The object is under the rug.)
5. A encomenda ficou debaixo do balcão. (The package stayed under the counter.)