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

No.

While the spelling, grammar, and core meaning (the contraction of the preposition em and the feminine demonstrative essa) are identical, there is a difference in typical usage. In Brazilian Portuguese, "nessa" is frequently used to refer to objects or time periods close to the speaker (proximal), whereas in Continental Portuguese, a stricter distinction is maintained, using "nesta" for proximal items and "nessa" only for items at a medium distance (medial).

Brazilian Portuguese Examples

1. O que tem nessa caneta? (What is in this pen?)
2. Eu gosto dessa blusa. (I like this blouse.)
3. Nessa semana, eu vou viajar. (This week, I am going to travel.)
4. Nessa parte do livro, é legal. (In that part of the book, it is cool.)
5. Você viu o que tem nessa sacola? (Did you see what is in this bag?)

Continental Portuguese Examples

1. O que há nesta caneta? (What is in this pen?)
2. Gosto desta blusa. (I like this blouse.)
3. Nesta semana, vou viajar. (This week, I am going to travel.)
4. Nessa parte do livro, é fixe. (In that part of the book, it is cool.)
5. Viste o que há nesta sacola? (Did you see what is in this bag?)