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

Yes

The spelling, meaning, and grammatical category of the word "boné" are identical in both Brazilian and Continental Portuguese. The only difference lies in pronunciation—specifically in the prosody and rhythm. In Brazilian Portuguese, the word is part of a more syllable-timed rhythm with clear, open vowels. In Continental Portuguese, the word is subject to the different patterns of vowel reduction and sentence-level stress characteristic of European Portuguese, often resulting in a more clipped sound.

Brazilian Portuguese Examples

1. Eu perdi meu boné no parque. (I lost my cap in the park.)
2. Ele sempre usa boné quando vai à praia. (He always wears a cap when he goes to the beach.)
3. Você viu o meu boné azul? (Did you see my blue cap?)
4. Aquele boné está muito estiloso. (That cap is very stylish.)
5. Esqueci meu boné na praia. (I forgot my cap at the beach.)

Portuguese (Portugal) Examples

1. Eu perdi o meu boné no parque. (I lost my cap in the park.)
2. Ele usa sempre um boné quando vai à praia. (He always wears a cap when he goes to the beach.)
3. Viste o meu boné azul? (Did you see my blue cap?)
4. O boné dele é muito giro. (His cap is very stylish.)
5. Preciso de comprar um boné novo para o verão. (I need to buy a new cap for the summer.)