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

Yes

The only differences between the use of "luz" in Brazilian and Continental Portuguese are in pronunciation and regional accent. The spelling, meaning, and grammatical function of the word remain identical. In Brazil, the vowel sound is typically more open and the cadence of the word follows Brazilian prosody, whereas in Portugal, the pronunciation may be slightly more closed or influenced by the specific regional accent of the speaker.

Brazilian Portuguese Examples

1. Apaga a luz antes de dormir. (Turn off the light before sleeping.)
2. A luz do sol tá muito forte hoje. (The sunlight is very strong today.)
3. A gente ficou sem luz ontem à noite. (We were without power last night.)
4. Essa luz tá muito fraquinha. (This light is very dim.)
5. Ela tem uma luz própria. (She has her own light/inner glow.)

Continental Portuguese Examples

1. Apaga a luz antes de ires dormir. (Turn off the light before you go to sleep.)
2. A luz do sol está bastante intensa hoje. (The sunlight is quite intense today.)
3. Houve um corte de energia durante a tempestade. (There was a power outage during the storm.)
4. Preciso de luz para conseguir ler. (I need light to be able to read.)
5. A luz do candeeiro é muito fraca. (The light from the lamp is very weak.)