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

Yes

The spelling, meaning, and grammatical function of "festa" are identical in both Brazilian and Continental Portuguese. The only difference lies in pronunciation. In Brazilian Portuguese, the vowels tend to be more "open" and the rhythm is more syllabic. In Continental Portuguese, the unstressed vowels are often "closed" or reduced, making the word sound more clipped or shortened.

Brazilian Portuguese Examples

1. A festa ontem foi muito legal. (The party yesterday was very cool.)
2. Eu vou fazer uma festa de aniversário. (I am going to have a birthday party.)
3. A festa estava uma bagunça. (The party was a mess.)
4. Você vai na festa de sábado? (Are you going to the party on Saturday?)
5. Tem muita gente na festa. (There are many people at the party.)

Continental Portuguese Examples

1. A festa de ontem foi muito bacana. (The party yesterday was very cool.)
2. Vou organizar uma festa de aniversário. (I am going to organize a birthday party.)
3. A festa estava uma confusão. (The party was a mess.)
4. Vais à festa de sábado? (Are you going to the party on Saturday?)
5. Há muita gente na festa. (There are many people at the party.)