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

Yes

The word "palco" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. It refers to a stage, a platform, or a metaphorical setting for an event. The only difference is in pronunciation: Brazilian Portuguese tends to have more open vowels and a more melodic, syllable-timed rhythm, whereas Continental Portuguese is more stress-timed, often resulting in more significant vowel reduction (making the unstressed "o" at the end sound even more like a subtle "u").

Brazilian Portuguese Examples

1. O cantor subiu ao palco com muita energia. (The singer went on stage with lots of energy.)
2. A banda está montando o palco para o festival. (The band is setting up the stage for the festival.)
3. Esse assunto virou palco para polêmicas. (This subject became a stage for controversies.)
4. As luzes do palco estavam muito fortes. (The stage lights were very bright.)
5. O ator se sente em casa quando está no palco. (The actor feels at home when he is on stage.)

Portuguese (Portugal) Examples

1. O músico apresentou-se no palco do teatro. (The musician performed on the theater stage.)
2. O palco ficou vazio logo após o espetáculo. (The stage became empty right after the show.)
3. Estão a montar o palco para o concerto de amanhã. (They are setting up the stage for tomorrow's concert.)
4. A peça de teatro decorre num palco circular. (The play takes place on a circular stage.)
5. Os músicos subiram ao palco sob uma chuva de aplausos. (The musicians went on stage to a shower of applause.)