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

No.

While the fundamental meaning, spelling, and grammar of "descer" are identical in both dialects, there are differences in typical usage and pronunciation. In Brazil, "descer" is frequently used colloquially to mean "to go to" a specific destination that is geographically or socially "lower" (e.g., "descer ao centro"), whereas in Portugal, the verb is used more strictly to denote physical downward movement. Additionally, the pronunciation differs: Brazilian Portuguese tends to feature more open vowels and a more pronounced "r," while Continental Portuguese is characterized by significant vowel reduction (making unstressed vowels sound much more closed or even swallowed).

Brazilian Portuguese Examples

1. Vou descer ao shopping agora. (I'm going down to the mall now.)
2. Vou descer no ponto. (I'm getting off at the stop.)
3. O preço da gasolina desceu muito. (The price of gas went down a lot.)
4. Ele desceu o morro correndo. (He ran down the hill.)
5. Eu vou descer do ônibus. (I'm going to get off the bus.)

Continental Portuguese Examples

1. Vou ao shopping agora. (I'm going to the mall now.)
2. Vou descer na paragem. (I'm getting off at the stop.)
3. O preço da gasolina baixou muito. (The price of gas went down a lot.)
4. Ele desceu a colina a correr. (He ran down the hill.)
5. Eu vou descer do autocarro. (I'm going to get off the bus.)