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

Yes

The word "sou" is the first-person singular present indicative of the verb ser. There are no differences in its meaning, grammar, or spelling between Brazilian and European Portuguese. The only difference is in pronunciation: in Brazil, the diphthong "ou" is typically more open and clearly articulated [oʊ], whereas in Portugal, the vowel sound is often more closed or even reduced to a single vowel [o] depending on the speaker's regional accent.

Brazilian Portuguese Examples

1. Eu sou brasileiro. (I am Brazilian.)
2. Eu sou muito legal. (I am very nice/cool.)
3. Eu sou o dono do cachorro. (I am the owner of the dog.)
4. Eu sou o responsável por isso. (I am the one responsible for this.)
5. Eu sou professor. (I am a teacher.)

European Portuguese Examples

1. Eu sou português. (I am Portuguese.)
2. Eu sou muito porreiro. (I am very cool.)
3. Eu sou o dono do cão. (I am the owner of the dog.)
4. Eu sou o responsável por isto. (I am the one responsible for this.)
5. Eu sou professor. (I am a teacher.)