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

Yes

The only difference between "peixe" in Brazilian and Continental Portuguese is the pronunciation. In Brazil, the diphthong "ei" is typically pronounced with more open and distinct vowels. In Portugal, the vowels are more "closed" or reduced, resulting in a more subtle, clipped sound. The spelling, meaning, and grammatical function of the word are identical in both dialects.

Brazilian Portuguese Examples:

1. Eu adoro comer peixe no almoço. (I love eating fish at lunch.)
2. Tem um peixe muito bonito nesse aquário. (There is a very beautiful fish in this aquarium.)
3. O peixe está muito fresquinho hoje. (The fish is very fresh today.)
4. Nós fomos pescar e pegamos um peixe enorme. (We went fishing and caught an enormous fish.)
5. Você viu aquele peixe no rio? (Did you see that fish in the river?)

Continental Portuguese Examples:

1. Eu estou a comer peixe. (I am eating fish.)
2. Há muito peixe no aquário. (There is a lot of fish in the aquarium.)
3. O peixe está muito fresco. (The fish is very fresh.)
4. Ele comprou um peixe grande no mercado. (He bought a big fish at the market.)
5. Viste aquele peixe? (Did you see that fish?)