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

Yes

The word "ritmo" is identical in meaning, spelling, and grammar in both Brazilian and European Portuguese. The only difference is in pronunciation. In Brazilian Portuguese, the final "o" is typically pronounced as a soft "u" (/ˈrit.mu/). In European Portuguese, the final "o" is even more reduced and often becomes nearly silent or a very short, neutral sound, and the "t" is pronounced with a more dental articulation.

Brazilian Portuguese Examples

1. Adorei o ritmo dessa música. (I loved the rhythm of this song.)
2. Você precisa pegar o ritmo do trabalho. (You need to get into the rhythm of the work.)
3. O ritmo de vida aqui é muito acelerado. (The rhythm of life here is very fast.)
4. Ele dança com um ritmo incrível. (He dances with an incredible rhythm.)
5. A bateria deu o ritmo para a banda. (The drums gave the rhythm to the band.)

European Portuguese Examples

1. Adorei o ritmo desta música. (I loved the rhythm of this song.)
2. Tu precisas de apanhar o ritmo do trabalho. (You need to catch the rhythm of the work.)
3. O ritmo de vida aqui é muito acelerado. (The rhythm of life here is very fast.)
4. Ele dança com um ritmo incrível. (He dances with an incredible rhythm.)
5. A bateria deu o ritmo à banda. (The drums gave the rhythm to the band.)