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

No.

While the physical meaning of "grossas" (thick) is identical in both dialects, there is a difference in typical usage regarding personality and behavior. In Brazilian Portuguese, "grossas" is the most common, everyday way to describe people who are rude, blunt, or impolite. In Continental Portuguese, while "grossas" can be used to describe something coarse or vulgar, the standard word used to describe a person's rude behavior is "grosseiras."

Brazilian Portuguese

1. As cordas são muito grossas. (The ropes are very thick.)
2. Elas foram grossas comigo na loja. (They were rude to me at the store.)
3. As camadas de gordura estão grossas. (The layers of fat are thick.)
4. Não aguento pessoas grossas. (I can't stand rude people.)
5. Use as canetas grossas para o cartaz. (Use the thick pens for the poster.)

Continental Portuguese

1. As cordas são muito grossas. (The ropes are very thick.)
2. Elas foram grosseiras comigo na loja. (They were rude to me at the store.)
3. As camadas de gordura estão grossas. (The layers of fat are thick.)
4. Não aguento pessoas grosseiras. (I can't stand rude people.)
5. Use as canetas grossas para o cartaz. (Use the thick pens for the poster.)