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

Yes

The word "energia" is identical in meaning, spelling, and grammatical function in both Brazilian and Continental Portuguese. The only difference is in pronunciation. In Brazilian Portuguese, the vowels are typically more open and clearly articulated. In Continental Portuguese, unstressed vowels (such as the "e" in the second syllable) are often "reduced" or "closed," making them sound much shorter or almost swallowed.

Brazilian Portuguese Examples

1. Ela tem muita energia para trabalhar. (She has a lot of energy to work.)
2. A conta de energia subiu muito este mês. (The electricity bill went up a lot this month.)
3. Preciso de uma dose de energia para o treino. (I need a dose of energy for the workout.)
4. Essa música me dá muita energia positiva. (This music gives me a lot of positive energy.)
5. O bairro ficou sem energia por causa da chuva. (The neighborhood lost power because of the rain.)

Continental Portuguese Examples

1. Ela tem uma energia contagiante. (She has a contagious energy.)
2. A conta da eletricidade chegou hoje. (The electricity bill arrived today.)
3. É necessário investir em energia renovável. (It is necessary to invest in renewable energy.)
4. Esta música transmite-me muita energia. (This music transmits much energy to me.)
5. Ficou sem luz na zona toda. (The whole area lost power.)