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

No

The meaning, grammar, and spelling of "ambos" are identical in both Brazilian and Continental Portuguese. The difference lies in typical usage and register. In Brazil, "ambos" is often perceived as formal, literary, or academic; in everyday casual conversation, Brazilians much more frequently use "os dois" to express the same idea. In Portugal, "ambos" is used naturally and frequently in both formal and informal, everyday speech.

Brazilian Portuguese (using "ambos" in its natural, formal/written context):

1. Ambos os projetos foram aprovados. (Both projects were approved.)
2. Ambos os alunos passaram na prova. (Both students passed the test.)
3. Ambos os lados chegaram a um acordo. (Both sides reached an agreement.)
4. Ambos os livros são muito interessantes. (Both books are very interesting.)
5. Ambos os documentos estão prontos. (Both documents are ready.)

Portuguese (using "os dois" to express the same idea, as is common in natural, casual speech):

1. Os dois projetos foram aprovados. (Both projects were approved.)
2. Os dois alunos passaram no exame. (Both students passed the exam.)
3. Os dois lados chegaram a um acordo. (Both sides reached an agreement.)
4. Os dois livros são muito interessantes. (Both books are very interesting.)
5. Os dois documentos estão prontos. (Both documents are ready.)