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

No

While the spelling, meaning, and grammatical function of "diremos" (the first-person plural future indicative of the verb dizer) are identical in both dialects, there are differences in pronunciation and typical usage:

• Usage (Register): In Brazilian Portuguese, "diremos" is often perceived as formal, literary, or even slightly archaic. In everyday spoken Brazilian Portuguese, people much more frequently use the compound future "vamos dizer." In Continental Portuguese, "diremos" is used naturally in both formal writing and standard daily conversation.
• Pronunciation: In Continental Portuguese, the unstressed "e" is often heavily reduced (nearly silent), and the final "s" is pronounced as a "sh" sound (/ʃ/). In Brazilian Portuguese, the "e" is more clearly articulated, and the final "s" is typically pronounced as /s/.

Brazilian Portuguese Examples (Using "diremos" in more formal or written contexts)

1. Nós diremos a verdade perante o tribunal. (We will tell the truth before the court.)
2. Diremos as conclusões no relatório final. (We will say the conclusions in the final report.)
3. Não diremos nada sem a vossa autorização. (We will not say anything without your authorization.)
4. Amanhã diremos o veredito oficial. (Tomorrow we will say the official verdict.)
5. Diremos o que for determinado pela lei. (We will say what is determined by the law.)

Continental Portuguese Examples (Using "diremos" in natural, everyday contexts)

1. Nós diremos a verdade a ele. (We will tell him the truth.)
2. Diremos tudo o que sabemos. (We will say everything we know.)
3. Não diremos o teu segredo a ninguém. (We won't tell your secret to anyone.)
4. Em breve diremos as novidades. (Soon we will say the news.)
5. O que diremos se ele perguntar? (What will we say if he asks?)