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

No.

The difference between the two lies in spelling and pronunciation. In Brazilian Portuguese, the word is spelled judô, using a circumflex accent to explicitly indicate a closed "o" sound. In Continental Portuguese, the standard spelling is judo, without the accent. While the pronunciation in both variants is similar, the lack of an accent in Portugal often leads to a slightly different phonetic realization of the final vowel depending on the regional accent.

Brazilian Portuguese examples:

• Eu treino judô todos os dias. (I train judo every day.)
• Ele é um faixa preta de judô muito respeitado. (He is a very respected black belt in judo.)
• A aula de judô foi cancelada hoje. (The judo class was cancelled today.)
• Meu filho começou a praticar judô na escola. (My son started practicing judo at school.)
• Você já participou de um campeonato de judô? (Have you ever participated in a judo championship?)

Continental Portuguese examples:

• Eu treino judo todos os dias. (I train judo every day.)
• Ele é um faixa preta de judo muito respeitado. (He is a very respected black belt in judo.)
• A aula de judo foi cancelada hoje. (The judo class was cancelled today.)
• O meu filho começou a praticar judo no ginásio. (My son started practicing judo at the gym.)
• Já foste a um campeonato de judo? (Have you ever been to a judo championship?)