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

No

While the meaning, grammar, and spelling of "creio" are identical in both varieties, there is a difference in typical usage and register. In Brazil, "creio" is often perceived as being very formal, literary, or specifically tied to religious contexts (e.g., "Creio em Deus"). In everyday Brazilian conversation, the word "acho" (I think/I believe) is the standard way to express an opinion. In Portugal, "creio" is used more frequently in standard, polite, or professional speech to express an opinion without necessarily sounding overly formal or religious.

Brazilian Portuguese

1. Creio que ele virá à festa. (I believe he will come to the party.)
2. Creio que o projeto será aprovado. (I believe the project will be approved.)
3. Creio em Deus. (I believe in God.)
4. Creio que o carro está quebrado. (I believe the car is broken.)
5. Creio que você tem razão. (I believe you are right.)

European Portuguese

1. Acho que ele vem à festa. (I think he is coming to the party.)
2. Acho que o projeto vai ser aprovado. (I think the project will be approved.)
3. Creio em Deus. (I believe in God.)
4. Acho que o carro está avariado. (I think the car is broken.)
5. Acho que tens razão. (I think you are right.)