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

Yes

The only difference between Brazilian and Continental Portuguese regarding the word "grande" is pronunciation. In Brazilian Portuguese, the final "e" is typically pronounced as a high, closed vowel, sounding like /i/ (e.g., "gran-djee" or "gran-dee"). In Continental Portuguese, the final "e" is unstressed and undergoes significant reduction, often becoming a near-silent schwa /ə/ or disappearing entirely, making the word sound more like "grand'."

Brazilian Portuguese Examples

1. O meu cachorro é muito grande. (My dog is very big.)
2. Ele é um grande profissional. (He is a great professional.)
3. A festa ficou grande demais. (The party became too big.)
4. Ele é um grande cara. (He is a great guy.)
5. O erro foi muito grande. (The error was very big.)

Portuguese Examples

1. O meu cão é muito grande. (My dog is very big.)
2. Ele é um grande profissional. (He is a great professional.)
3. A festa ficou demasiado grande. (The party became too big.)
4. Ele é um grande tipo. (He is a great guy.)
5. O erro foi muito grande. (The error was very big.)