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

No

While the spelling, grammar, and primary meanings (referring to the country or the bird) are identical, the typical usage differs significantly. In Brazil, "peru" is a very common and highly vulgar slang term for the penis. In Portugal, while the word is understood due to media influence, it is not a standard slang term for that anatomy; the word is almost exclusively used in its literal sense (the bird or the country).

Brazilian Portuguese

1. O Peru é um país muito bonito. (Peru is a very beautiful country.)
2. O peru é uma ave de grande porte. (The turkey is a large bird.)
3. Eu adoro comer peru no Natal. (I love eating turkey at Christmas.)
4. O Peru tem uma história fascinante. (Peru has a fascinating history.)
5. Aquele cara é um peru. (That guy is a [vulgar slang].)

Portuguese (Portugal)

1. O Peru é um país muito bonito. (Peru is a very beautiful country.)
2. O peru é uma ave de grande porte. (The turkey is a large bird.)
3. Eu adoro comer peru no Natal. (I love eating turkey at Christmas.)
4. O Peru tem uma história fascinante. (Peru has a fascinating history.)
5. Aquele tipo é um idiota. (That guy is an idiot.)