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

Yes

The word "intensamente" is spelled, defined, and grammatically used identically in both Brazilian and Continental Portuguese. The only difference is pronunciation. In Brazilian Portuguese, the vowels are generally more open and clearly articulated. In Continental Portuguese, there is a much higher degree of vowel reduction; unstressed vowels (like the "e" in the middle or at the end of the word) are often shortened, closed, or almost entirely silent in natural speech.

Brazilian Portuguese Examples

1. Eu amo intensamente a minha família. (I love my family intensely.)
2. Ela estudou intensamente para o vestibular. (She studied intensely for the college entrance exam.)
3. Vamos aproveitar a vida intensamente! (Let's enjoy life intensely!)
4. A chuva caiu intensamente durante a noite. (The rain fell intensely during the night.)
5. Ele trabalha de forma muito intensa. (He works in a very intense manner.)

European Portuguese Examples

1. Eu amo profundamente a minha família. (I love my family deeply.)
2. Ela estudou imenso para o exame. (She studied immensely for the exam.)
3. Temos de viver cada momento com toda a intensidade. (We have to live every moment with all the intensity.)
4. A chuva caiu com muita força durante a noite. (The rain fell with great force during the night.)
5. Ele trabalha imenso durante a semana. (He works immensely during the week.)