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

Yes.

The word "favor" is identical in spelling, meaning, and grammatical category (noun) in both Brazilian and Continental Portuguese. The differences are strictly limited to pronunciation:

• Vowels: In Brazilian Portuguese, the vowels are generally more open and clearly articulated. In Continental Portuguese, vowels are often more closed or reduced (for example, the "a" may sound more like a neutral "uh").
• The "r" sound: Depending on the region of Brazil, the final "r" can be a flap, a retroflex, or even silent, whereas in Portugal, it is typically a more distinct, often uvular or tapped sound.

Brazilian Portuguese Examples

1. Você me faz um favor? (Will you do me a favor?)
2. Por favor, me empresta esse livro. (Please, lend me this book.)
3. Eu te peço um favor. (I am asking you a favor.)
4. Ele fez isso como um favor para mim. (He did that as a favor to me.)
5. Por favor, não esqueça o meu nome. (Please, don't forget my name.)

Continental Portuguese Examples

1. Fazes-me um favor? (Will you do me a favor?)
2. Por favor, empresta-me este livro. (Please, lend me this book.)
3. Eu peço-te um favor. (I am asking you a favor.)
4. Ele fez isto como um favor para mim. (He did this as a favor to me.)
5. Por favor, não te esqueças do meu nome. (Please, don't forget my name.)