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

Yes

The word "compro" is identical in meaning, spelling, and grammatical function in both Brazilian and Continental Portuguese; it is the first-person singular present indicative of the verb comprar. The only difference is in pronunciation. In Brazilian Portuguese, the unstressed "o" at the end of the word is typically pronounced as a clear [u] sound. In Continental Portuguese, unstressed vowels are much more reduced and "closed," meaning the "o" in "compro" is often much shorter or almost swallowed in natural, fast-paced speech.

Brazilian Portuguese Examples

1. Eu compro pão todo dia. (I buy bread every day.)
2. Eu compro roupas na promoção. (I buy clothes on sale.)
3. Eu compro frutas na feira. (I buy fruits at the market.)
4. Eu compro meu celular novo. (I buy my new cell phone.)
5. Eu compro doces para as crianças. (I buy sweets for the children.)

Continental Portuguese Examples

1. Compro pão todos os dias. (I buy bread every day.)
2. Compro roupa em promoção. (I buy clothes on sale.)
3. Compro fruta na feira. (I buy fruit at the market.)
4. Compro o meu telemóvel novo. (I buy my new mobile phone.)
5. Compro doces para as crianças. (I buy sweets for the children.)