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

No

While the spelling and fundamental meaning of "essa" are the same, there is a significant difference in usage and pronunciation. In Brazilian Portuguese, the grammatical distinction between este/esta (near the speaker) and esse/essa (near the listener) is often blurred; Brazilians frequently use "essa" to refer to objects held by or physically close to themselves. In Continental Portuguese, this distinction is strictly observed. Furthermore, Brazilian pronunciation features more open, melodic vowels, whereas European Portuguese tends to reduce or "swallow" unstressed vowels, making the word sound more clipped and short.

Brazilian Portuguese

1. Essa caneta aqui é sua? (Is this pen here yours?)
2. Eu não gosto dessa cor. (I don't like this color.)
3. Essa comida está muito boa. (This food is very good.)
4. Você viu essa notícia? (Did you see this news?)
5. Essa ideia é excelente. (This idea is excellent.)

Continental Portuguese

1. Esta caneta aqui é tua? (Is this pen here yours?)
2. Eu não gosto desta cor. (I don't like this color.)
3. Esta comida está muito boa. (This food is very good.)
4. Viste esta notícia? (Did you see this news?)
5. Esta ideia é excelente. (This idea is excellent.)