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

No

While the meaning, spelling, and core definition of "avisar" (to notify, to warn, or to let someone know) are identical in both dialects, there are significant differences in grammar and typical usage regarding how the word is applied in a sentence.

In Brazilian Portuguese, it is standard to use proclisis (placing the object pronoun before the verb, e.g., "me avisa") and to use subject pronouns as direct objects in colloquial speech (e.g., "avisa ele"). In Continental Portuguese, the standard is enclisis (placing the pronoun after the verb, e.g., "avisa-me") and the use of oblique forms (e.g., "avisa-o"). Additionally, while the spelling is the same, the pronunciation of the vowels differs; Brazilian Portuguese tends to have more open vowels, while Continental Portuguese features more closed, unstressed vowels.

Brazilian Portuguese Examples

1. Me avisa quando você chegar. (Let me know when you arrive.)
2. Eu vou avisar ele da festa. (I'm going to tell him about the party.)
3. Avisa lá se você vai poder ir. (Let them know if you'll be able to go.)
4. Ele me avisou que o ônibus ia atrasar. (He told me the bus was going to be late.)
5. Pode avisar a Maria, por favor? (Can you notify Maria, please?)

Continental Portuguese Examples

1. Avisa-me quando chegares. (Let me know when you arrive.)
2. Vou avisá-lo da festa. (I'm going to tell him about the party.)
3. Avisa-os se vais poder ir. (Let them know if you'll be able to go.)
4. Ele avisou-me que o autocarro ia atrasar. (He told me the bus was going to be late.)
5. Podes avisar a Maria, por favor? (Can you notify Maria, please?)