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

No

While "nossa" functions identically in both dialects as a feminine singular possessive pronoun (meaning "our"), there is a difference in typical usage regarding its use as an interjection. In Brazil, "Nossa!" is an incredibly common, standalone interjection used to express surprise, shock, or awe. In Portugal, while the full religious phrase "Nossa Senhora!" is used, the shortened "Nossa!" is much less frequent as a primary, standalone exclamation; Portuguese speakers more typically rely on interjections like "Fogo," "Caramba," or "Epá" to express the same sentiment.

Brazilian Portuguese Usage

1. Nossa, que susto! (Wow, what a scare!)
2. Nossa, eu não acredito nisso. (Wow, I don't believe that.)
3. Esta é a nossa casa. (This is our house.)
4. Nossa, que calor está fazendo! (Wow, it's so hot!)
5. Nossa, como você cresceu! (Wow, how you have grown!)

Continental Portuguese Usage

1. Fogo, que susto! (Damn, what a scare!)
2. Caramba, eu não acredito nisso. (Goodness, I don't believe that.)
3. Esta é a nossa casa. (This is our house.)
4. Epá, que calor que está! (Man, it's so hot!)
5. Epá, como tu cresceste! (Man, how you have grown!)