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

Yes

The word "época" is identical in spelling, meaning, and grammatical function in both Brazilian and European Portuguese. The only differences are in pronunciation, specifically regarding the prosody (rhythm) and the phonetic realization of the surrounding unstressed vowels. In Brazilian Portuguese, the rhythm is more syllable-timed and the vowels tend to be more open, whereas in European Portuguese, the rhythm is more stress-timed, which can lead to a more "closed" or swallowed sound in the unstressed syllables surrounding the word.

Brazilian Portuguese Examples

1. Naquela época, eu morava em São Paulo. (At that time, I lived in São Paulo.)
2. A época de férias está chegando. (The vacation season is approaching.)
3. Era uma época muito boa para viajar. (It was a very good time to travel.)
4. Gosto muito desta época do ano. (I really like this time of year.)
5. Na época em que eu era criança, as coisas eram mais simples. (In the time when I was a child, things were simpler.)

European Portuguese Examples

1. Naquela época, eu vivia no Porto. (At that time, I lived in Porto.)
2. A época de férias está a chegar. (The vacation season is arriving.)
3. Foi uma época muito boa para viajar. (It was a very good time to travel.)
4. Gosto muito desta época do ano. (I really like this time of year.)
5. Na época em que ia à escola, as coisas eram mais simples. (In the time when I went to school, things were simpler.)