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

Yes

The word "raiva" is identical in spelling, meaning, and grammatical gender in both Brazilian and Continental Portuguese. The only difference is pronunciation. In Brazilian Portuguese, the vowels are typically more open, and the "ai" diphthong is pronounced with more clarity and resonance. In Continental Portuguese, the vowels (especially unstressed ones) tend to be more closed or reduced, and the rhythm of the word is more staccato. While the word itself is the same, the grammatical placement of pronouns around it (clitics) differs between the two dialects (e.g., me dá raiva in Brazil vs. dá-me raiva in Portugal).

Brazilian Portuguese Examples

1. Eu estou com muita raiva dele. (I am very angry with him.)
2. Isso me dá muita raiva! (This makes me so angry!)
3. Não fica com raiva de mim, por favor. (Don't be angry with me, please.)
4. Ela está com uma raiva que não passa. (She is feeling an anger that won't go away.)
5. Ele descarregou a raiva no trabalho. (He took his anger out on his work.)

Continental Portuguese Examples

1. Estou com uma raiva enorme! (I am feeling enormous rage!)
2. Isso dá-me uma raiva terrível. (This gives me terrible anger.)
3. Não fiques com raiva de mim. (Don't be angry with me.)
4. Ele estava cheio de raiva. (He was full of rage.)
5. A raiva dele é muito visível. (His anger is very visible.)