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

Yes

The word "ovo" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. The only difference is pronunciation. In Brazilian Portuguese, the vowels are generally more open and clearly articulated. In Continental Portuguese, there is a much stronger tendency toward vowel reduction; consequently, the unstressed "o" in the second syllable is pronounced as a very closed sound, almost like a "u" ([ˈovu]), and the initial "o" is also more closed than in most Brazilian dialects.

Brazilian Portuguese Examples

1. Eu gosto de comer ovo mexido no café da manhã. (I like to eat scrambled eggs for breakfast.)
2. Você pode comprar uma dúzia de ovos? (Can you buy a dozen eggs?)
3. O ovo cozido está na geladeira. (The boiled egg is in the fridge.)
4. Ele quebrou o ovo sem querer. (He broke the egg by accident.)
5. Preciso de um ovo para fazer esse bolo. (I need an egg to make this cake.)

Continental Portuguese Examples

1. Eu gosto de comer ovo mexido ao pequeno-almoço. (I like to eat scrambled eggs for breakfast.)
2. Podes comprar uma dúzia de ovos? (Can you buy a dozen eggs?)
3. O ovo cozido está no frigorífico. (The boiled egg is in the fridge.)
4. Ele partiu o ovo sem querer. (He broke the egg by accident.)
5. Preciso de um ovo para fazer este bolo. (I need an egg to make this cake.)