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

Yes

The word "roupa" is identical in meaning, spelling, and grammatical function in both Brazilian and Continental Portuguese. The only difference lies in pronunciation. Brazilian Portuguese tends to be more "syllable-timed," with vowels being more open and clearly articulated. In contrast, Continental Portuguese is more "stress-timed," meaning unstressed vowels (like the final "a" in roupa) are often reduced, shortened, or even swallowed, making the word sound much more clipped to a Brazilian ear.

Brazilian Portuguese Examples

1. Eu preciso comprar uma roupa nova. (I need to buy new clothes.)
2. Essa roupa ficou muito bem em você. (That clothing looks very good on you.)
3. Onde está a minha roupa suja? (Where is my dirty laundry?)
4. Ela não sabe que roupa usar na festa. (She doesn't know what clothes to wear to the party.)
5. Guarde sua roupa no armário, por favor. (Put your clothes in the closet, please.)

Continental Portuguese Examples

1. Preciso de comprar roupa nova. (I need to buy new clothes.)
2. Essa roupa fica-te muito bem. (That clothing looks very good on you.)
3. Onde está a minha roupa suja? (Where is my dirty laundry?)
4. Ela não sabe que roupa vestir para a festa. (She doesn't know what clothes to wear to the party.)
5. Guarda a tua roupa no armário, por favor. (Put your clothes in the closet, please.)