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

Yes

The word dizer is identical in meaning, spelling, and grammar in both Brazilian and European Portuguese. The only difference is in pronunciation. Brazilian Portuguese tends to have more open, clear vowels and a "syllable-timed" rhythm, making the word sound more melodic. Continental Portuguese features more closed or "reduced" vowels and a "stress-timed" rhythm, where unstressed syllables are often swallowed or shortened, making the word sound more clipped to a Brazilian ear.

Brazilian Portuguese Examples

1. O que você quer dizer com isso? (What do you mean by that?)
2. Ele disse que não vem à festa. (He said he isn't coming to the party.)
3. Eu não disse nada para ele. (I didn't say anything to him.)
4. Você pode me dizer a verdade? (Can you tell me the truth?)
5. Ela está dizendo que está cansada. (She is saying that she is tired.)

European Portuguese Examples

1. O que é que estás a dizer com isso? (What are you saying with that?)
2. Ele disse que não vem à festa. (He said he isn't coming to the party.)
3. Eu não disse nada a ele. (I didn't say anything to him.)
4. Podes dizer-me a verdade? (Can you tell me the truth?)
5. Ela está a dizer que está cansada. (She is saying that she is tired.)