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

No

While the spelling and the core meaning of "prometo" (I promise) are identical in both varieties, there are significant differences in pronunciation and typical usage/grammar:

• Pronunciation: In Continental Portuguese, unstressed vowels are much more "closed" or reduced, often sounding almost like a "schwa" (an indistinct, neutral sound). In Brazilian Portuguese, vowels are generally more "open" and clearly articulated.
• Usage and Grammar: The primary difference lies in clitic placement (how pronouns attach to the verb). In Brazil, it is natural to place the object pronoun before the verb (e.g., "Eu te prometo"). In Portugal, the standard is to place the pronoun after the verb (e.g., "Prometo-te"). Additionally, Brazilians frequently use the contraction "pra" (for para) and the near future (vou fazer), whereas Portuguese speakers are more likely to use "a" (the preposition) and the formal future tense (farei).

Brazilian Portuguese Examples

1. Eu te prometo que vou te ligar amanhã. (I promise you I will call you tomorrow.)
2. Prometo que não vou contar pra ninguém. (I promise I won't tell anyone.)
3. Eu prometo que vou fazer o meu melhor. (I promise I will do my best.)
4. Prometo que vou chegar logo. (I promise I will arrive soon.)
5. Eu te prometo que vai dar tudo certo. (I promise you that everything will work out.)

Continental Portuguese Examples

1. Prometo-te que te ligarei amanhã. (I promise you I will call you tomorrow.)
2. Prometo que não vou contar a ninguém. (I promise I won't tell anyone.)
3. Prometo que farei o meu melhor. (I promise I will do my best.)
4. Prometo que chegarei depressa. (I promise I will arrive soon.)
5. Prometo-te que tudo correrá bem. (I promise you that everything will go well.)