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

Yes

The word "vazio" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. The only difference is in pronunciation. In Brazilian Portuguese, the pronunciation is generally more "open," with more distinct and elongated vowel sounds and a more melodic rhythm. In Continental Portuguese, the pronunciation is more "closed"; unstressed vowels are often reduced or "swallowed," and the overall cadence is more consonant-heavy and staccato.

Brazilian Portuguese Examples

1. O copo está vazio. (The glass is empty.)
2. Sinto um vazio no meu coração. (I feel an emptiness in my heart.)
3. O estacionamento do shopping está vazio hoje. (The mall parking lot is empty today.)
4. Esse argumento é totalmente vazio. (That argument is totally hollow/empty.)
5. O apartamento ficou vazio depois que ele saiu. (The apartment became empty after he left.)

Continental Portuguese Examples

1. O copo está vazio. (The glass is empty.)
2. Sinto um vazio no meu coração. (I feel an emptiness in my heart.)
3. O parque de estacionamento do centro comercial está vazio hoje. (The shopping center parking lot is empty today.)
4. Este argumento é totalmente vazio. (This argument is totally hollow/empty.)
5. O apartamento ficou vazio após a sua saída. (The apartment became empty after his departure.)