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

Yes

The spelling, meaning, and grammatical function of "arroz" are identical in both dialects. The difference is strictly phonetic. In Brazilian Portuguese, the final "z" is a voiced alveolar fricative (/z/), sounding like the "z" in "zebra." In Continental Portuguese, the final "z" is typically unvoiced, sounding like "sh" (/ʃ/), as in "shoe." Additionally, the "rr" sound often differs, with many Brazilian dialects using a more aspirated "h" sound, while Portuguese speakers typically use a more guttural or trilled sound.

Brazilian Portuguese

1. Eu gosto muito de arroz com feijão. (I like rice and beans very much.)
2. Você pode fazer o arroz para o jantar? (Can you make the rice for dinner?)
3. O arroz está ficando pronto. (The rice is getting ready.)
4. Eu comprei um pacote de arroz no mercado. (I bought a bag of rice at the market.)
5. Tem muito arroz na panela. (There is a lot of rice in the pot.)

Continental Portuguese

1. Gosto muito de arroz com feijão. (I like rice and beans very much.)
2. Podes fazer o arroz para o jantar? (Can you make the rice for dinner?)
3. O arroz está a ficar pronto. (The rice is getting ready.)
4. Comprei um pacote de arroz no supermercado. (I bought a bag of rice at the supermarket.)
5. Há muito arroz na panela. (There is a lot of rice in the pot.)