Is the word bem-vinda the same in Brazilian and European Portuguese?

Yes.

The word "bem-vinda" is identical in meaning, grammar, and spelling 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 often "closed" or reduced, which can make the word sound more clipped or muffled to a Brazilian ear.

Brazilian Portuguese Examples

1. Seja bem-vinda à nossa casa! (Welcome to our house!)
2. Você é muito bem-vinda na nossa equipe. (You are very welcome to our team.)
3. Seja bem-vinda ao Brasil! (Welcome to Brazil!)
4. Sinta-se bem-vinda aqui sempre que quiser. (Feel welcome here whenever you want.)
5. Que bom que você veio, seja bem-vinda! (So glad you came, welcome!)

Continental Portuguese Examples

1. Seja bem-vinda à nossa morada. (Welcome to our home.)
2. És muito bem-vinda na nossa equipa. (You are very welcome to our team.)
3. Seja bem-vinda ao nosso país. (Welcome to our country.)
4. Sente-te bem-vinda em nossa casa. (Feel welcome in our house.)
5. Bem-vinda à nossa aldeia! (Welcome to our village!)