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

Yes

The word "preciso" is identical in spelling, meaning, and grammar in both Brazilian and Continental Portuguese. It can function as the first-person singular present indicative of the verb precisar (meaning "I need") or as an adjective (meaning "precise," "accurate," or "necessary"). The only differences are phonetic: in Brazilian Portuguese, the vowels are generally more open and the pronunciation is more syllable-timed. In Continental Portuguese, unstressed vowels (such as the "e") are often reduced or nearly silent, and the rhythm is more stress-timed.

Brazilian Portuguese Examples

1. Eu preciso de um café agora. (I need a coffee right now.)
2. O diagnóstico do médico foi muito preciso. (The doctor's diagnosis was very precise.)
3. É preciso ter cuidado ao dirigir. (It is necessary to be careful while driving.)
4. Eu preciso terminar meu dever de casa. (I need to finish my homework.)
5. Eu preciso carregar meu celular. (I need to charge my cell phone.)

Continental Portuguese Examples

1. Eu preciso de um café agora. (I need a coffee right now.)
2. O diagnóstico do médico foi muito preciso. (The doctor's diagnosis was very precise.)
3. É necessário ter cuidado ao conduzir. (It is necessary to be careful while driving.)
4. Eu preciso de terminar o meu trabalho de casa. (I need to finish my homework.)
5. Eu preciso de carregar o meu telemóvel. (I need to charge my mobile phone.)