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

No

While the spelling and the dictionary definition of "pimenta" are the same in both dialects, there is a significant difference in typical usage. In Brazil, "pimenta" is the generic term used to refer to chili peppers (the fruit/vegetable that provides heat). In Portugal, "pimenta" refers almost exclusively to the spice (such as black pepper or ground pepper). To refer to the spicy chili peppers themselves, a person from Portugal would typically use the words "malagueta" or "piripiri."

Brazilian Portuguese Examples

1. Eu adoro comer comida com muita pimenta. (I love eating food with a lot of chili.)
2. Essa pimenta está muito forte! (This chili is very strong!)
3. Você pode me passar o molho de pimenta? (Can you pass me the hot sauce?)
4. Coloquei pimenta demais no meu ovo. (I put too much chili in my egg.)
5. Essa pimenta malagueta é bem ardida. (This malagueta chili is very spicy.)

Continental Portuguese Examples

1. Eu adoro comer comida com muito piripiri. (I love eating food with a lot of chili.)
2. Essa malagueta está muito forte! (This chili is very strong!)
3. Podes passar-me o molho de piripiri? (Can you pass me the chili sauce?)
4. Pus piripiri a mais nos meus ovos. (I put too much chili in my eggs.)
5. Esta malagueta é bastante picante. (This chili is quite spicy.)