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

No

While the word sento (the first-person singular present indicative of the verb sentar) is spelled and defined the same way in both dialects, there is a significant difference in typical usage and grammar regarding how it interacts with reflexive pronouns. In Brazilian Portuguese, it is standard to use proclisis (placing the pronoun before the verb: me sento). In Continental Portuguese, the standard is enclisis (placing the pronoun after the verb: sento-me).

Brazilian Portuguese Examples

1. Eu me sento na cadeira. (I sit in the chair.)
2. Eu me sento sempre perto de você. (I always sit near you.)
3. Eu me sento no sofá para descansar. (I sit on the sofa to rest.)
4. Eu me sento na mesa para comer. (I sit at the table to eat.)
5. Eu me sento aqui agora. (I am sitting here now.)

Continental Portuguese Examples

1. Eu sento-me na cadeira. (I sit in the chair.)
2. Eu sento-me sempre junto a ti. (I always sit near you.)
3. Eu sento-me no sofá para descansar. (I sit on the sofa to rest.)
4. Eu sento-me à mesa para comer. (I sit at the table to eat.)
5. Eu sento-me aqui agora. (I am sitting here now.)