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

Yes

The meaning, spelling, and grammatical classification of "cabelo" are identical in both Brazilian and Continental Portuguese. The difference is found exclusively in pronunciation. In Brazil, the vowels are typically more open and the rhythm of speech is more "syllable-timed," making the word sound more melodic. In Portugal, the vowels are more closed or reduced, and the rhythm is "stress-timed," which can make the unstressed syllables sound much softer or almost swallowed.

Brazilian Portuguese Examples

1. Eu preciso cortar o meu cabelo. (I need to cut my hair.)
2. Ela tem o cabelo muito comprido. (She has very long hair.)
3. Seu cabelo está muito bagunçado hoje! (Your hair is very messy today!)
4. Eu adoro o seu cabelo cacheado. (I love your curly hair.)
5. Ele passou um produto para deixar o cabelo macio. (He applied a product to make the hair soft.)

Continental Portuguese Examples

1. Vou cortar o cabelo. (I'm going to cut my hair.)
2. Ela tem o cabelo muito longo. (She has very long hair.)
3. O teu cabelo está muito desarrumado. (Your hair is very messy.)
4. Gosto muito do teu cabelo encaracolado. (I like your curly hair very much.)
5. Ele aplicou um produto para o cabelo ficar suave. (He applied a product to make the hair soft/smooth.)