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

Yes

The word "coentro" has the same meaning, spelling, and grammatical function in both Brazilian and Continental Portuguese. The primary difference lies in pronunciation. In Brazilian Portuguese, the vowels tend to be more open and clearly articulated. In Continental Portuguese, unstressed vowels are often "reduced" or swallowed; therefore, the "o" in "coentro" sounds much more closed and brief, almost merging the syllables more tightly than a Brazilian speaker would.

Brazilian Portuguese Examples

1. Eu não suporto o gosto de coentro. (I can't stand the taste of cilantro.)
2. Você prefere coentro ou salsa? (Do you prefer cilantro or parsley?)
3. Coloque um pouco de coentro picado na comida. (Put a little chopped cilantro in the food.)
4. O cheiro do coentro está muito forte aqui. (The smell of cilantro is very strong in here.)
5. Vou comprar coentro e cebolinha no mercado. (I'm going to buy cilantro and green onions at the market.)

Continental Portuguese Examples

1. Eu não suporto o sabor de coentro. (I can't stand the taste of coriander.)
2. Preferes coentro ou salsa? (Do you prefer coriander or parsley?)
3. Podes pôr um pouco de coentro na sopa? (Can you put a little coriander in the soup?)
4. Este molho tem demasiado coentro. (This sauce has too much coriander.)
5. Tenho de ir ao supermercado comprar coentro. (I have to go to the supermarket to buy coriander.)