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

No

While "menor" functions similarly as an adjective in both dialects (meaning "less" or "smaller"), there are significant differences in typical usage. In Brazil, "menor" is widely used as a noun to refer to an underage person or a juvenile, often carrying a specific connotation in news reporting. In Portugal, the term is almost always used as an adjective, and when referring to a person, "menor de idade" is much more common. Additionally, regarding physical size and value, Brazilians frequently use "menor," whereas Portuguese speakers naturally prefer "mais pequeno" (smaller) or "mais baixo" (lower/less).

Brazilian Portuguese

1. O menor preço que encontrei foi este. (The lowest price I found was this one.)
2. O menor foi detido pela polícia. (The minor was detained by the police.)
3. Este é o menor quarto da casa. (This is the smallest room in the house.)
4. Ele tem o menor interesse na aula. (He has the least interest in the class.)
5. A venda é proibida para menores. (The sale is forbidden for minors.)

Continental Portuguese

1. O preço mais baixo que encontrei foi este. (The lowest price I found was this one.)
2. O menor de idade foi detido pela polícia. (The minor was detained by the police.)
3. Este é o quarto mais pequeno da casa. (This is the smallest room in the house.)
4. Ele tem muito pouco interesse na aula. (He has very little interest in the class.)
5. A venda é proibida a menores de idade. (The sale is forbidden to minors.)