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

Yes

The word "cliente" is identical in spelling, meaning, and grammar in both Brazilian and Continental Portuguese. It functions as a common-gender noun (o cliente / a cliente) in both dialects. The only difference lies in pronunciation:

• Brazilian Portuguese: The vowels are generally more open and the "e" at the end of words is often pronounced clearly as /i/ or /e/. The nasal "en" is pronounced with a distinct nasal resonance.
• Continental Portuguese: The vowels are much more closed, and the final "e" is often reduced to a very short, almost silent /ɨ/ sound. The "en" is also more clipped.

Brazilian Portuguese Examples

1. O cliente está esperando na recepção. (The client is waiting in the reception.)
2. Eu tenho um cliente novo. (I have a new client.)
3. O cliente não gostou do produto. (The client did not like the product.)
4. Precisamos atender o cliente logo. (We need to serve the client soon.)
5. O cliente ligou para a loja. (The client called the store.)

Portuguese Examples

1. O cliente está a esperar na receção. (The client is waiting at the reception.)
2. Tenho um novo cliente. (I have a new client.)
3. O cliente não gostou do produto. (The client did not like the product.)
4. É preciso atender o cliente depressa. (It is necessary to serve the client quickly.)
5. O cliente ligou para a loja. (The client called the store.)