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

No.

While the meaning and spelling of "perdoa" are identical in both dialects, there are significant differences in usage and grammar. In Brazil, the 2nd person imperative form (perdoa) is frequently used to address você (the informal/standard "you"), whereas in Portugal, the distinction is strictly maintained: perdoa is used only for tu, and perdoe is used for você or formal address. Additionally, Brazilians typically use proclisis (placing the pronoun before the verb, e.g., "me perdoa"), while Portuguese speakers naturally use enclisis (placing the pronoun after the verb, e.g., "perdoa-me").

Brazilian Portuguese Examples

1. Me perdoa, eu esqueci. (Forgive me, I forgot.)
2. Ele nunca perdoa ninguém. (He never forgives anyone.)
3. Perdoa o meu atraso. (Forgive my lateness.)
4. Você me perdoa por isso? (Do you forgive me for this?)
5. Deus perdoa todos os pecados. (God forgives all sins.)

Continental Portuguese Examples

1. Perdoa-me, eu esqueci-me. (Forgive me, I forgot.)
2. Ele nunca perdoa ninguém. (He never forgives anyone.)
3. Perdoe o meu atraso. (Forgive my lateness. — Using the formal form for 'você')
4. Tu perdoas-me por isto? (Do you forgive me for this?)
5. Deus perdoa todos os pecados. (God forgives all sins.)