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

Yes

The word "quero" is identical in meaning, grammar, and spelling in both Brazilian and Continental Portuguese. The primary difference lies in pronunciation.

In Brazilian Portuguese, the vowels are typically more open and the syllables are pronounced more clearly. The "e" in "quero" is usually an open or mid-vowel ([k'e.ɾu]). In Continental Portuguese, vowels are often reduced or "swallowed" in unstressed positions. This can make the "e" sound much more closed, or in rapid speech, the vowel may almost disappear, making the word sound more like "kru" ([k'ɾu]).

Brazilian Portuguese Usage

1. Eu quero um café, por favor. (I want a coffee, please.)
2. Eu não quero sair hoje. (I don't want to go out today.)
3. Eu quero muito viajar para a Europa. (I really want to travel to Europe.)
4. Eu quero comprar um carro novo. (I want to buy a new car.)
5. Eu quero que você venha aqui. (I want you to come here.)

Continental Portuguese Usage

1. Eu queria um café, por favor. (I would like a coffee, please. — Note: "queria" is used more naturally for politeness.)
2. Não quero sair hoje. (I don't want to go out today.)
3. Tenho muita vontade de viajar para a Europa. (I really want to travel to Europe. — Note: "ter vontade" is a very natural way to express intense desire.)
4. Quero comprar um carro novo. (I want to buy a new car.)
5. Quero que venhas cá. (I want you to come here. — Note: "venhas" is the correct conjugation for "tu," and "cá" is more common than "aqui" in this context.)