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

Yes

The word "nariz" is identical in spelling, meaning, and grammatical gender in both Brazilian and Continental Portuguese. The only difference is pronunciation. In Brazilian Portuguese, the vowels are generally more open, and the rhythm of speech is syllable-timed. In Continental Portuguese, the vowels are more closed, and the rhythm is stress-timed. While the "z" at the end is often pronounced as an "s" in many Brazilian regions, the phonetic quality of the entire word differs due to the way vowels and consonants are articulated.

Brazilian Portuguese Examples

1. Eu tenho um resfriado e meu nariz está entupido. (I have a cold and my nose is stuffed up.)
2. Ele limpou o nariz com um lenço. (He wiped his nose with a tissue.)
3. O cheiro da comida chegou até o meu nariz. (The smell of the food reached my nose.)
4. Ela tem um nariz muito bonito. (She has a very beautiful nose.)
5. Não fique com o nariz empinado! (Don't be so stuck-up! / Literally: Don't keep your nose upturned!)

Continental Portuguese Examples

1. Estou com um resfriado e o meu nariz está entupido. (I have a cold and my nose is stuffed up.)
2. Ele limpou o nariz com um lenço. (He wiped his nose with a tissue.)
3. O cheiro da comida chegou ao meu nariz. (The smell of the food reached my nose.)
4. Ela tem um nariz muito bonito. (She has a very beautiful nose.)
5. Não andes com o nariz empinado! (Don't go around with your nose in the air!)