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

Yes

The word "vestido" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. The only difference lies in pronunciation. In Brazilian Portuguese, the vowels are generally more "open" and clearly articulated. In Continental Portuguese, unstressed vowels are much more "closed" or "reduced," often sounding almost swallowed. Additionally, the "s" in certain positions (like at the end of a syllable) is pronounced as a "sh" sound ([ʃ]) in Portugal, whereas in many parts of Brazil, it is pronounced as a soft "s" or "z".

Brazilian Portuguese Examples

1. Eu comprei um vestido novo ontem. (I bought a new dress yesterday.)
2. Ela está sempre muito bem vestida. (She is always very well dressed.)
3. Esse vestido azul fica lindo em você. (This blue dress looks beautiful on you.)
4. Onde você comprou esse vestido de festa? (Where did you buy that party dress?)
5. Eu me vesti rápido para não perder o ônibus. (I dressed quickly so I wouldn't miss the bus.)

Continental Portuguese Examples

1. Eu comprei um vestido novo ontem. (I bought a new dress yesterday.)
2. Ela está sempre muito bem vestida. (She is always very well dressed.)
3. Esse vestido azul fica lindo em ti. (This blue dress looks beautiful on you.)
4. Onde é que compraste esse vestido de festa? (Where is it that you bought that party dress?)
5. Eu vesti-me rápido para não perder o autocarro. (I dressed myself quickly so I wouldn't miss the bus.)