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

No

While the core meanings and spelling of "meio" are identical in both dialects (referring to the middle, the center, or the fraction one-half), there is a difference in typical usage and accompanying grammar. In Brazil, "meio" is the most common way to use an adverb meaning "somewhat" or "a bit" (e.g., meio triste). While a Portuguese person understands this, they naturally prefer using "um pouco" or "um bocado" for the same purpose. Furthermore, when using "meio" in this adverbial sense, the sentence structure often changes due to differences in pronoun placement (clitics) between the two countries.

Brazilian Portuguese Usage

1. Ela está meio cansada. (She is a bit tired.)
2. O preço está meio alto. (The price is a bit high.)
3. Eu me senti meio mal depois do almoço. (I felt a bit unwell after lunch.)
4. A situação está meio complicada. (The situation is a bit complicated.)
5. O filme é meio chato. (The movie is a bit boring.)

Continental Portuguese Usage

1. Ela está um pouco cansada. (She is a bit tired.)
2. O preço está um bocado alto. (The price is a bit/quite high.)
3. Eu senti-me um pouco mal depois do almoço. (I felt a bit unwell after lunch.)
4. A situação está um pouco complicada. (The situation is a bit complicated.)
5. O filme é um bocado chato. (The movie is a bit boring.)