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

No

Differences in Meaning and Usage

The primary difference is in usage and connotation.

In Brazilian Portuguese, "quebrada" is a very common slang term used to refer to one's neighborhood, community, or "hood" (typically a peripheral or suburban area). While it can still refer to a geographical ravine, its cultural identity in Brazil is heavily tied to urban identity and social roots.

In Continental Portuguese, the word "quebrada" is not used to refer to a neighborhood. In Portugal, the word is almost exclusively used in a geological sense (a ravine, gorge, or small valley) or to describe something that is broken. Furthermore, when describing an object that is broken, a Portuguese person would much more naturally use the word "partido" instead of "quebrado."

Brazilian Portuguese Examples (Slang usage)

1. "A minha quebrada é o melhor lugar do mundo." (My hood is the best place in the world.)
2. "Ele é um cria da quebrada." (He is a local from the hood.)
3. "Tudo acontece na quebrada." (Everything happens in the hood.)
4. "A quebrada está em festa hoje." (The hood is celebrating today.)
5. "Eu respeito muito a minha quebrada." (I respect my hood very much.)

Continental Portuguese Examples (Equivalent expressions)

1. "O meu bairro é o melhor lugar do mundo." (My neighborhood is the best place in the world.)
2. "Ele é daqui do bairro." (He is from this neighborhood.)
3. "Tudo acontece no bairro." (Everything happens in the neighborhood.)
4. "O bairro está em festa hoje." (The neighborhood is celebrating today.)
5. "Eu respeito muito o meu bairro." (I respect my neighborhood very much.)