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

Yes

The word "papel" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. The only difference is in pronunciation, specifically regarding the final "l":

• Brazilian Portuguese: The "l" at the end of a syllable or word is vocalized, sounding like a "u" (phonetically [paˈpɛw]).
• Continental Portuguese: The "l" is pronounced as a true lateral consonant, where the tip of the tongue touches the alveolar ridge (phonetically [paˈpɛl]).

Brazilian Portuguese Examples

1. Eu preciso de um papel para escrever. (I need a piece of paper to write.)
2. O papel dela na empresa é muito importante. (Her role in the company is very important.)
3. Joga o papel no lixo. (Throw the paper in the trash.)
4. O papel de parede está ficando velho. (The wallpaper is getting old.)
5. O papel higiênico acabou. (The toilet paper ran out.)

Continental Portuguese Examples

1. Eu preciso de um papel para escrever. (I need a piece of paper to write.)
2. O papel dela na empresa é muito importante. (Her role in the company is very important.)
3. Deita o papel no lixo. (Throw the paper in the trash.)
4. O papel de parede está a ficar velho. (The wallpaper is getting old.)
5. O papel higiénico acabou. (The toilet paper ran out.)