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

Yes

The word is identical in meaning, spelling, and grammar across both dialects. The only differences are phonetic. In Brazilian Portuguese, the vowels are generally more open and clearly articulated, and the unstressed final "o" is pronounced clearly as a "u" sound. In Continental Portuguese, there is significant vowel reduction (where unstressed vowels become shorter or "closed"), and the "s" before a consonant (as in esposo) is pronounced with a "sh" sound (/ʃ/).

Brazilian Portuguese (using "esporso" in formal or polite contexts):

1. O meu esposo é um excelente médico. (My husband is an excellent doctor.)
2. Ela apresentou o esposo para os amigos. (She introduced her husband to her friends.)
3. O esposo da vizinha é muito educado. (The neighbor's husband is very polite.)
4. Gostaria de convidar o seu esposo para o jantar. (I would like to invite your husband to dinner.)
5. O nome do esposo consta no documento. (The husband's name appears on the document.)

Portuguese (using "marido" for natural, everyday usage):

1. O meu marido está a trabalhar agora. (My husband is working now.)
2. O teu marido já chegou a casa? (Has your husband arrived home yet?)
3. O marido dela é um tipo muito porreiro. (Her husband is a very cool guy.)
4. Fui ao centro comercial com o meu marido. (I went to the shopping mall with my husband.)
5. O meu marido está cá em casa. (My husband is here at home.)