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

Yes

The word "outra" is identical in meaning, spelling, and grammatical function in both Brazilian and European Portuguese. The only difference lies in pronunciation.

In Brazilian Portuguese, the word is typically pronounced with more open vowels and a syllable-timed rhythm, meaning the final "a" is clearly and distinctly articulated.

In Continental Portuguese, the pronunciation is more "closed" and stress-timed. Unstressed vowels are often reduced or "swallowed." In the word "outra," the final "a" is often pronounced as a very short, neutral, and nearly silent sound ([ɐ]).

Brazilian Portuguese Examples:

1. Eu quero outra cor. (I want another color.)
2. Você tem outra ideia? (Do you have another idea?)
3. Vou pegar outra caneta. (I'm going to grab another pen.)
4. Ela está usando outra roupa. (She is wearing another outfit.)
5. Eu vou comprar outra camisa. (I am going to buy another shirt.)

European Portuguese Examples:

1. Eu quero outra cor. (I want another color.)
2. Tens outra ideia? (Do you have another idea?)
3. Vou buscar outra caneta. (I am going to get another pen.)
4. Ela está a usar outra roupa. (She is wearing another outfit.)
5. Eu vou comprar outra camisa. (I am going to buy another shirt.)