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

Yes

The word "entendi" is identical in meaning, grammar, and spelling in both Brazilian and Continental Portuguese. The only differences lie in pronunciation, specifically regarding how unstressed vowels are articulated. In Brazil, the unstressed "e" in the second syllable is often more clearly pronounced or slightly more open, whereas in Portugal, unstressed vowels tend to be more "reduced" or neutralized, sometimes sounding almost silent or like a very short "i" sound.

Brazilian Portuguese Examples

1. Entendi o que você disse. (I understood what you said.)
2. Ah, entendi agora! (Ah, I get it now!)
3. Eu não entendi nada dessa aula. (I didn't understand anything of this class.)
4. Não entendi por que você ficou bravo. (I didn't understand why you got angry.)
5. Entendi perfeitamente o seu ponto. (I understood your point perfectly.)

Portuguese (Portugal) Examples

Note: While "entendi" is used in Portugal, a Portuguese person would more naturally use "compreendi" in many contexts to express the same idea, and would use "tu/teu" instead of "você/seu" for informal address.

1. Compreendi o que disseste. (I understood what you said.)
2. Ah, agora compreendi! (Ah, now I understand!)
3. Não compreendi nada desta aula. (I didn't understand anything of this class.)
4. Não compreendi por que ficaste bravo. (I didn't understand why you got angry.)
5. Compreendi perfeitamente o teu ponto. (I understood your point perfectly.)