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

No

While the spelling and the fundamental meaning of "estou" (the first-person singular of the verb estar) are identical in both Brazilian and Continental Portuguese, the answer is No because there are significant differences in typical usage.

In Brazil, "estou" is most commonly used with the gerund to express ongoing actions (e.g., estou falando). In Portugal, the standard usage for ongoing actions is "estou" followed by the preposition a + infinitive (e.g., estou a falar). Additionally, in casual Brazilian speech, "estou" is frequently reduced to "tô," a feature much less common in standard or formal European Portuguese.

Brazilian Portuguese natural usage:

1. Estou muito cansado. (I am very tired.)
2. Estou fazendo o almoço. (I am making lunch.)
3. Tô chegando agora. (I'm arriving now.)
4. Estou com muita saudade de você. (I miss you very much.)
5. Não estou entendendo nada. (I am not understanding anything.)

Continental Portuguese natural usage:

1. Estou muito cansado. (I am very tired.)
2. Estou a fazer o almoço. (I am making lunch.)
3. Estou a chegar agora. (I am arriving now.)
4. Estou com muitas saudades de ti. (I miss you very much.)
5. Não estou a perceber nada. (I am not understanding anything.)