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

No

While the spelling, grammar, and core definition of "sério" are identical in both Brazilian and Continental Portuguese, there are differences in pronunciation and typical usage.

Pronunciation: In Brazilian Portuguese, vowels are generally more open and clearly articulated. In Continental Portuguese, unstressed vowels undergo significant reduction; the "i" in "sério" may become very subtle or almost disappear, sounding more like "sér'o."

Usage: In Brazil, "Sério?" is a very common, standalone interjection meaning "Really?" or "Are you serious?". In Portugal, while "Sérío?" is understood, it is much more natural and idiomatic to use the phrase "A sério?" to express the same disbelief or to seek confirmation. Additionally, when using the word in a continuous sense (e.g., "Are you being serious?"), Brazilians use the gerund (falando), whereas Portuguese people use the prepositional construction (a falar).

Brazilian Portuguese Examples

1. "Ele é um homem muito sério." (He is a very serious man.)
2. "Você está falando sério?" (Are you being serious?)
3. "Sério? Eu não acredito!" (Really? I don't believe it!)
4. "Isso é um assunto muito sério." (This is a very serious matter.)
5. "Não seja tão sério, vamos nos divertir." (Don't be so serious, let's have some fun.)

Continental Portuguese Examples

1. "Ele é um homem muito sério." (He is a very serious man.)
2. "Estás a falar a sério?" (Are you speaking seriously?)
3. "A sério? Não consigo acreditar!" (Really? I can't believe it!)
4. "Isto é um assunto muito sério." (This is a very serious matter.)
5. "Não sejas tão sério, vamos divertir-nos." (Don't be so serious, let's have some fun.)