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

Yes

The word "paisagem" is identical in both Brazilian and Continental Portuguese in terms of spelling, grammar, and meaning. The only difference lies in pronunciation. In Brazilian Portuguese, the vowels tend to be more "open" and the rhythm of speech is more syllable-timed. In Continental Portuguese, the unstressed vowels (such as the "e" in the penultimate syllable) are often much more "closed" or reduced, sometimes becoming nearly silent, which gives the language a more stress-timed rhythm.

Brazilian Portuguese

1. A paisagem da Serra do Mar é maravilhosa. (The landscape of Serra do Mar is wonderful.)
2. Eu adoro tirar fotos da paisagem. (I love taking photos of the landscape.)
3. Essa paisagem parece um quadro. (This landscape looks like a painting.)
4. A paisagem mudou muito com a chuva. (The landscape changed a lot with the rain.)
5. A paisagem urbana de São Paulo é muito agitada. (The urban landscape of São Paulo is very busy.)

Continental Portuguese

1. A paisagem da Serra da Arrábida é deslumbrante. (The landscape of Serra da Arrábida is stunning.)
2. Gosto de tirar fotografias da paisagem. (I like taking photographs of the landscape.)
3. Esta paisagem parece uma pintura. (This landscape looks like a painting.)
4. A paisagem alterou-se bastante com a chuva. (The landscape changed quite a bit with the rain.)
5. Observámos a paisagem urbana de Lisboa. (We observed the urban landscape of Lisbon.)