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

No

While the core definition of "chato" (annoying or boring) is shared by both dialects, there are significant differences in pronunciation and typical usage:

• Pronunciation: In most regions of Brazil, the "t" in "chato" is palatalized, meaning it is pronounced with a "ch" sound (like cha-cho). In Portugal, the "t" remains dental or alveolar, sounding much closer to the English "t" in "top."
• Usage (Objects): In Brazilian Portuguese, "chato" is commonly used to describe an object that has lost air pressure, such as a tire (o pneu está chato). In Portugal, this usage is not standard; a Portuguese person would use "furado" (punctured) or "desinflado" (deflated).
• Usage (Synonyms): While "chato" is perfectly understood in Portugal, Portuguese speakers naturally rely on a wider variety of specific synonyms to express different levels of boredom or annoyance, such as seca, secante, or maçador.

Brazilian Portuguese Examples

1. Esse filme é muito chato. (This movie is very boring.)
2. Ele é um cara muito chato. (He is a very annoying guy.)
3. O pneu do carro está chato. (The car tire is flat.)
4. Que chato que você não pode vir! (How annoying/unfortunate that you can't come!)
5. Não seja chato, vamos sair! (Don't be annoying, let's go out!)

Continental Portuguese Examples

1. Este filme é uma seca. (This movie is a bore/very boring.)
2. Ele é um tipo muito secante. (He is a very annoying guy.)
3. O pneu do carro está furado. (The car tire is punctured/flat.)
4. Que chatice que tu não podes vir! (How annoying/unfortunate that you can't come!)
5. Não sejas maçador, vamos sair! (Don't be a bore, let's go out!)