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

Yes.

The word is identical in meaning, spelling, and grammatical gender. The only difference lies in pronunciation. In Brazilian Portuguese, vowels tend to be more open and the rhythm is more melodic; the unstressed "e" in "arqui-te-ta" is clearly articulated. In Continental Portuguese, unstressed vowels are often reduced or almost entirely suppressed, making the word sound more "clipped" or staccato.

Brazilian Portuguese

1. Ela é uma arquiteta muito talentosa. (She is a very talented architect.)
2. Preciso contratar uma arquiteta para reformar minha casa. (I need to hire an architect to renovate my house.)
3. A arquiteta entregou o projeto hoje. (The architect delivered the project today.)
4. Minha irmã acabou de se formar como arquiteta. (My sister just graduated as an architect.)
5. A arquiteta está desenhando a planta. (The architect is drawing the floor plan.)

Continental Portuguese

1. Ela é uma arquiteta muito talentosa. (She is a very talented architect.)
2. Preciso contratar uma arquiteta para remodelar a minha casa. (I need to hire an architect to remodel my house.)
3. A arquiteta entregou o projeto hoje. (The architect delivered the project today.)
4. A minha irmã acabou de se licenciar em arquitetura. (My sister just graduated in architecture.)
5. A arquiteta está a desenhar a planta. (The architect is drawing the floor plan.)