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

Yes.

The spelling, meaning, and grammar of the word "Brasil" are identical in both Brazilian and Continental Portuguese. The only difference lies in pronunciation. In Brazil, the vowels are generally more open and the rhythm is syllable-timed, often resulting in a slight "u" sound at the end of the word (e.g., [bɾaˈziw]). In Portugal, the vowels are more closed or reduced, and the rhythm is stress-timed, which can make the unstressed syllables sound much shorter.

Brazilian Portuguese Examples

1. Eu amo o Brasil. (I love Brazil.)
2. O Brasil é muito grande. (Brazil is very big.)
3. Eu quero viajar para o Brasil. (I want to travel to Brazil.)
4. O pessoal do Brasil é muito legal. (The people from Brazil are very cool.)
5. O Brasil tem praias muito bacanas. (Brazil has very cool beaches.)

Portuguese (Portugal) Examples

1. Eu adoro o Brasil. (I adore Brazil.)
2. O Brasil é imenso. (Brazil is immense.)
3. Eu pretendo visitar o Brasil. (I intend to visit Brazil.)
4. A malta do Brasil é muito porreira. (The folks from Brazil are very cool.)
5. O Brasil tem praias fantásticas. (Brazil has fantastic beaches.)