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

Yes

The word "desse" is a contraction of the preposition de and the demonstrative pronoun esse. There are no differences in its spelling, grammar, or fundamental meaning between the two dialects. The only difference is pronunciation:

• In Brazil, the unstressed final "e" is typically pronounced as a high front unrounded vowel (sounding like an "i"), making the word sound like dess-ee ([ˈdɛsi]).
• In Portugal, the unstressed final "e" is often reduced to a very short, closed, or nearly silent sound, making the word sound more like dess ([ˈdɛs]).

Brazilian Portuguese Examples:

1. Eu não gosto desse carro. (I don't like that car.)
2. O preço desse celular está muito alto. (The price of this/that cell phone is very high.)
3. Não me fale desse assunto. (Don't talk to me about that subject.)
4. Tire o pé desse sofá. (Take your foot off that sofa.)
5. Você viu desse jeito? (Did you see it that way?)

Portuguese (Portugal) Examples:

1. Eu não gosto desse carro. (I don't like that car.)
2. O preço desse telemóvel está muito alto. (The price of that mobile phone is very high.)
3. Não me fales desse assunto. (Don't talk to me about that subject.)
4. Tira o pé desse sofá. (Take your foot off that sofa.)
5. Viste desse jeito? (Did you see it that way?)