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

Yes

The word "tanto" 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 the unstressed "o" is clearly articulated as a /u/ sound. In Continental Portuguese, unstressed vowels are more frequently reduced or "swallowed," making the word sound more clipped and the nasal "an" sound more closed.

Brazilian Portuguese Examples:

1. Eu te amo tanto. (I love you so much.)
2. Você tem tanto trabalho hoje! (You have so much work today!)
3. Não tinha tanto tempo assim para isso. (There wasn't that much time for that.)
4. Ele comeu tanto que ficou passando mal. (He ate so much that he started feeling sick.)
5. Tinha tanta gente na rua! (There were so many people on the street!)

Continental Portuguese Examples:

1. Eu amo-te tanto. (I love you so much.)
2. Tu tens tanto trabalho hoje! (You have so much work today!)
3. Não havia tanto tempo assim para isso. (There wasn't that much time for that.)
4. Ele comeu tanto que se sentiu mal. (He ate so much that he felt sick.)
5. Havia tanta gente na rua! (There were so many people on the street!)