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

No

While the core meaning of "saber" (to know information or a skill) is identical, there is a difference in typical usage regarding taste. In Portugal, "saber" is commonly used to describe the flavor of food (e.g., "sabe a chocolate"), whereas in Brazil, the verb "ter gosto de" is the standard expression. Additionally, there is a significant difference in pronunciation: Brazilian Portuguese features more open, clearly articulated vowels, while European Portuguese is more "stress-timed," which often leads to unstressed vowels being reduced or nearly "swallowed."

Brazilian Portuguese Examples:

1. Eu não sei o que aconteceu. (I don't know what happened.)
2. Você sabe onde fica o banheiro? (Do you know where the bathroom is?)
3. Eu quero saber a verdade. (I want to know the truth.)
4. Ela sabe falar inglês muito bem. (She knows how to speak English very well.)
5. Isso tem gosto de chocolate. (This tastes like chocolate.)

Continental Portuguese Examples:

1. Eu não sei o que aconteceu. (I don't know what happened.)
2. Tu sabes onde fica a casa de banho? (Do you know where the bathroom is?)
3. Eu quero saber a verdade. (I want to know the truth.)
4. Ela sabe falar inglês muito bem. (She knows how to speak English very well.)
5. Isto sabe a chocolate. (This tastes like chocolate.)