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

No

In Brazil, balada is a common colloquialism used to refer to a nightclub, a party, or the act of "going out" for a night of entertainment. In Portugal, the word is used almost exclusively to refer to the musical genre of a "ballad" (a slow, sentimental song). While both dialects use "balada" for the musical meaning, the widespread use of the word to mean "nightclub" or "party" is a specific characteristic of Brazilian Portuguese.

Brazilian Portuguese Usage

How a Brazilian would naturally use "balada" to refer to a night out or a club:

1. Vamos para uma balada hoje à noite? (Are we going to a club tonight?)
2. A balada estava muito cheia e barulhenta. (The nightclub was very crowded and noisy.)
3. Eu amo sair para balada com meus amigos. (I love going out clubbing with my friends.)
4. Essa balada é bem cara, melhor irmos em outro lugar. (This nightclub is quite expensive, better we go somewhere else.)
5. Ontem a balada foi incrível! (Yesterday's night out was amazing!)

European Portuguese Usage

How a Portuguese person would naturally express those same ideas using their own vocabulary:

1. Vamos à discoteca hoje à noite? (Are we going to the nightclub tonight?)
2. A discoteca estava muito cheia e barulhenta. (The nightclub was very crowded and noisy.)
3. Eu gosto de ir a festas com os meus amigos. (I like going to parties with my friends.)
4. Este clube é muito caro, é melhor irmos para outro lado. (This club is very expensive, it is better to go somewhere else.)
5. A festa de ontem foi incrível! (Yesterday's party was amazing!)