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

Yes

The only difference between the use of "famoso" in Brazilian Portuguese and Continental Portuguese is pronunciation. In both dialects, the word has the same meaning (famous/well-known), the same spelling, and the same grammatical function as an adjective.

In Brazilian Portuguese, the vowels are generally more "open" and the rhythm is more melodic. The final "o" is clearly articulated. In Continental Portuguese, unstressed vowels are much more reduced or "closed." The final "o" in "famoso" is pronounced as a very short, closed "u" sound and can even sound almost swallowed. Because the "s" is positioned between two vowels, it is pronounced as a voiced /z/ in both dialects.

Brazilian Portuguese Examples

1. Ele é um ator muito famoso. (He is a very famous actor.)
2. Eu não quero ser famoso. (I don't want to be famous.)
3. Esse restaurante é muito famoso aqui na cidade. (That restaurant is very famous here in the city.)
4. Você conhece aquele cantor famoso? (Do you know that famous singer?)
5. Ele ficou famoso de repente. (He became famous suddenly.)

Continental Portuguese Examples

1. Ele é um ator muito famoso. (He is a very famous actor.)
2. Eu não pretendo ser famoso. (I do not intend to be famous.)
3. Este restaurante é muito famoso aqui na cidade. (This restaurant is very famous here in the city.)
4. Tu conheces aquele cantor famoso? (Do you know that famous singer?)
5. Ele tornou-se famoso de repente. (He became famous suddenly.)