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

No.

While the fundamental meanings of "capa" (cover, cape, or cloak) are the same in both dialects, there are differences in typical usage. In Brazil, the diminutive "capinha" is much more common than "capa" when referring to small covers, such as those for mobile phones. Additionally, for rain protection, a Portuguese person would more naturally use the word "impermeável" instead of "capa de chuva."

Brazilian Portuguese

1. A capa do meu celular está riscada. (The cover of my cell phone is scratched.)
2. Pegue a sua capa de chuva. (Grab your raincoat.)
3. A capa do livro é muito bonita. (The book cover is very beautiful.)
4. Ele usa uma capa de super-herói. (He wears a superhero cape.)
5. A capa da revista é chamativa. (The magazine cover is eye-catching.)

Continental Portuguese

1. A capa do meu telemóvel está riscada. (The cover of my mobile phone is scratched.)
2. Veste o teu impermeável. (Put on your raincoat.)
3. A capa do livro é muito bonita. (The book cover is very beautiful.)
4. Ele usa uma capa de super-herói. (He wears a superhero cape.)
5. A capa da revista é chamativa. (The magazine cover is eye-catching.)