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

Yes

The meaning, grammar, and spelling of "grandes" are identical in both Brazilian and Continental Portuguese. The only difference lies in pronunciation:

• Brazilian Portuguese: The vowels tend to be more open, and the rhythm is more syllable-timed. The final "e" is often more audible or slightly more emphasized, and the nasal diphthong "an" is quite distinct and resonant.
• Continental Portuguese: The pronunciation is more "closed" and stress-timed. The final "e" is often heavily reduced or almost entirely silent, and the nasal sounds are much more subtle and compressed.

Brazilian Portuguese

1. Eles têm grandes planos para o futuro. (They have big plans for the future.)
2. As cidades grandes são muito barulhentas. (Big cities are very noisy.)
3. Ele fez grandes amizades na faculdade. (He made great friends in college.)
4. As crianças cresceram muito, estão grandes! (The kids grew a lot, they are big!)
5. Aquelas são grandes dificuldades para nós. (Those are big difficulties for us.)

Continental Portuguese

1. Eles têm grandes planos para o futuro. (They have big plans for the future.)
2. As cidades grandes são muito ruidosas. (Big cities are very noisy.)
3. Ele fez grandes amizades na universidade. (He made great friends at the university.)
4. As crianças cresceram imenso, estão grandes! (The kids grew immensely, they are big!)
5. Aquelas são grandes dificuldades para nós. (Those are big difficulties for us.)