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

Yes

The word "barata" is identical in meaning, spelling, and grammar in both Brazilian and European Portuguese. The only difference is in pronunciation:

• Brazilian Portuguese: The vowels are more "open" and clearly articulated. The "a" sounds are bright and distinct.
• European Portuguese: The vowels are more "closed" or "reduced." Unstressed vowels (like the final "a" in barata) are often shortened or muffled, sounding more like a neutral "uh" sound.

Brazilian Portuguese Examples

1. Vi uma barata na cozinha. (I saw a cockroach in the kitchen.)
2. Essa camiseta está muito barata. (This t-shirt is very cheap.)
3. Não aguento mais ver barata aqui em casa. (I can't stand seeing cockroaches here at home anymore.)
4. A passagem de ônibus foi bem barata. (The bus ticket was quite cheap.)
5. Essa loja sempre tem coisa barata. (This store always has cheap things.)

European Portuguese Examples

1. Vi uma barata na cozinha. (I saw a cockroach in the kitchen.)
2. Esta camisola está muito barata. (This sweater is very cheap.)
3. Não gosto de baratas no meu quarto. (I don't like cockroaches in my bedroom.)
4. O bilhete de autocarro foi bastante barato. (The bus ticket was quite cheap.)
5. Esta loja tem artigos muito baratos. (This shop has very cheap items.)