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

No.

The meaning and spelling of "agradecer" are identical in both dialects. However, the answer is No because there are significant differences in pronunciation and grammar/usage:

• Pronunciation: In Brazilian Portuguese, the vowels are more open and the syllables are articulated clearly. In European Portuguese, vowels are often reduced or "swallowed" (vowel reduction), making the word sound much more closed and consonant-heavy.
• Grammar/Usage: The primary difference lies in clitic placement (how pronouns attach to the verb). In Brazil, it is natural and common to use proclisis (placing the object pronoun before the verb, e.g., "te agradecer"). In Portugal, the standard is enclisis (placing the pronoun after the verb, e.g., "agradecer-te").

Brazilian Portuguese Examples

1. Eu quero te agradecer pelo presente. (I want to thank you for the gift.)
2. Ela agradeceu muito o apoio que recebeu. (She thanked the support she received very much.)
3. Não sei como agradecer por tanta gentileza. (I don't know how to thank [you] for such kindness.)
4. Eu vou agradecer ao professor pela aula. (I am going to thank the teacher for the class.)
5. A gente veio aqui para agradecer o convite. (We came here to thank [you] for the invitation.)

European Portuguese Examples

1. Quero agradecer-te pelo presente. (I want to thank you for the gift.)
2. Ela agradeceu muito o apoio que recebeu. (She thanked the support she received very much.)
3. Não sei como agradecer-te por tanta gentileza. (I don't know how to thank you for such kindness.)
4. Vou agradecer-lhe pela aula. (I am going to thank him/her for the class.)
5. Viemos aqui para agradecer à vossa equipa. (We came here to thank your team.)