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

Yes

The word "deste" is identical in both Brazilian and Continental Portuguese in terms of meaning, grammar, and spelling. It is the contraction of the preposition de (of) and the demonstrative pronoun este (this). The only difference is in pronunciation: in Brazilian Portuguese, the unstressed final "e" is frequently reduced or neutralized, often sounding like an "i" (making the word sound like des-tchee). In Continental Portuguese, the vowel is typically more clearly articulated.

Brazilian Portuguese Examples

1. Eu preciso descer deste ônibus. (I need to get off this bus.)
2. O leite deste refrigerador está frio. (The milk in this refrigerator is cold.)
3. O horário deste trem mudou. (The schedule of this train changed.)
4. O gosto deste café da manhã é bom. (The taste of this breakfast is good.)
5. A tela deste celular quebrou. (The screen of this cell phone broke.)

Continental Portuguese Examples

1. Eu preciso de sair deste autocarro. (I need to get off this bus.)
2. O leite deste frigorífico está frio. (The milk in this fridge is cold.)
3. O horário deste comboio mudou. (The schedule of this train changed.)
4. O sabor deste pequeno-almoço é bom. (The taste of this breakfast is good.)
5. O ecrã deste telemóvel partiu-se. (The screen of this mobile phone broke.)