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

Yes.

The spelling, meaning, and conjugation of the word "observar" are identical in both Brazilian and European Portuguese. The differences lie in pronunciation (specifically the rhythm and the openness of certain vowels) and the syntactic structure used when combining the verb with auxiliary verbs. While Brazilians typically use the gerund (observando), Portuguese people typically use the preposition "a" followed by the infinitive (a observar). Additionally, for the specific sense of "noticing" something, a Portuguese person is much more likely to use the synonym "reparar."

Brazilian Portuguese

1. Eu observei que você mudou o cabelo. (I noticed you changed your hair.)
2. É importante observar as regras do jogo. (It is important to observe the rules of the game.)
3. Ele estava observando os pássaros no parque. (He was observing the birds in the park.)
4. Você observou que ele estava nervoso? (Did you notice that he was nervous?)
5. Precisamos observar o comportamento dos animais. (We need to observe the behavior of the animals.)

European Portuguese

1. Reparei que mudaste o cabelo. (I noticed you changed your hair.)
2. É importante observar as regras do jogo. (It is important to observe the rules of the game.)
3. Ele estava a observar os pássaros no parque. (He was observing the birds in the park.)
4. Reparaste que ele estava nervoso? (Did you notice that he was nervous?)
5. Precisamos observar o comportamento dos animais. (We need to observe the behavior of the animals.)