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

No

While the primary meaning of "barato" (cheap/inexpensive) is identical in both dialects, there is a significant difference in usage and slang meaning. In Brazil, "barato" can be used as an adjective or noun to describe something that is "cool," "pleasant," "fun," or a "great experience" (e.g., "Que barato!"). In Portugal, "barato" is almost exclusively used to refer to low prices; using it to mean "cool" would be confusing to a Portuguese person.

Brazilian Portuguese Examples

1. Achei esse celular muito barato na promoção. (I found this cell phone very cheap on sale.)
2. Procuro um restaurante que seja bem barato. (I am looking for a restaurant that is very cheap.)
3. Cara, que show muito barato! (Man, what a really cool show!)
4. Que barato essa música nova! (How cool is this new song!)
5. O preço da gasolina está muito barato hoje. (The price of gas is very cheap today.)

Continental Portuguese Examples

1. Achei este telemóvel muito barato na promoção. (I found this mobile phone very cheap on sale.)
2. Procuro um restaurante que seja muito barato. (I am looking for a restaurant that is very cheap.)
3. Pá, que concerto espetacular! (Man, what a spectacular concert!)
4. Que fixe esta música nova! (How cool is this new song!)
5. O preço da gasolina está muito barato hoje. (The price of gas is very cheap today.)