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

No

While the spelling and the core meaning of "precisamos" (we need) are identical in both dialects, there are differences in pronunciation and typical usage.

Pronunciation: Brazilian Portuguese features more open, "musical" vowels, making the word easier to distinguish syllable by syllable. Continental Portuguese uses much more closed, reduced, or even suppressed vowels, which can make the middle syllables sound almost silent to an untrained ear.

Usage: In Brazil, it is very common in casual speech to omit the preposition "de" after the verb (e.g., precisamos fazer). In Portugal, the use of the preposition "de" is much more strictly maintained and is considered the standard (e.g., precisamos de fazer). Additionally, Brazilians frequently use the word "logo" to mean "soon," whereas a Portuguese person would more naturally use "depressa" (quickly) or "brevemente" (shortly) to convey similar timing.

Brazilian Portuguese Examples

1. Precisamos comprar um carro novo. (We need to buy a new car.)
2. Precisamos de ajuda com a mudança. (We need help with the move.)
3. Precisamos terminar esse projeto logo. (We need to finish this project soon.)
4. Precisamos comer alguma coisa agora. (We need to eat something now.)
5. Precisamos ver o resultado da prova. (We need to see the exam result.)

Portuguese (Portugal) Examples

1. Precisamos de comprar um carro novo. (We need to buy a new car.)
2. Precisamos de ajuda com a mudança. (We need help with the move.)
3. Precisamos de terminar esse projeto depressa. (We need to finish this project quickly.)
4. Precisamos de comer alguma coisa agora. (We need to eat something now.)
5. Precisamos de ver o resultado do exame. (We need to see the exam result.)