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

Yes

The word "cor" is identical in meaning, spelling, and grammar (it is a feminine noun) in both Brazilian and Continental Portuguese. The only difference is in pronunciation.

In Brazilian Portuguese, the vowel "o" is often pronounced more openly ([kɔɾ]), and the "r" at the end of the word varies by region, ranging from a retroflex "r" (similar to the American English "r") in the interior to an alveolar tap in Rio de Janeiro. In Continental Portuguese, the vowel "o" tends to be more closed or even reduced ([koɾ]), and the "r" is typically pronounced as an alveolar tap.

Brazilian Portuguese Examples

1. Essa cor é muito legal. (This color is very cool.)
2. Eu adoro essa cor de camiseta. (I love this color of t-shirt.)
3. Qual é a sua cor favorita? (What is your favorite color?)
4. Essa cor combinou muito com você. (This color really suited you.)
5. Tem uma cor diferente nessa parede. (There is a different color on this wall.)

Continental Portuguese Examples

1. Esta cor é muito fixe. (This color is very cool.)
2. Eu adoro esta cor de camisola. (I love this color of sweater/shirt.)
3. Qual é a tua cor preferida? (What is your favorite color?)
4. Esta cor fica-te muito bem. (This color looks very good on you.)
5. Há uma cor diferente nesta parede. (There is a different color on this wall.)