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

Yes

The word "avenida" is identical in meaning, spelling, and grammatical gender in both Brazilian and Continental Portuguese. The only difference is in pronunciation. In Brazilian Portuguese, the vowels are more open and clearly articulated, and the rhythm of the word is more melodic. In Continental Portuguese, unstressed vowels (especially the final "a") are often reduced or "swallowed," leading to a more closed and clipped pronunciation.

Brazilian Portuguese Examples

1. A avenida está lotada de gente. (The avenue is crowded with people.)
2. Você sabe onde fica a avenida principal? (Do you know where the main avenue is?)
3. Eu gosto de dirigir por essa avenida à noite. (I like driving along this avenue at night.)
4. Tem muita árvore nessa avenida. (There are many trees on this avenue.)
5. A avenida é muito barulhenta durante o dia. (The avenue is very noisy during the day.)

Continental Portuguese Examples

1. A avenida está cheia de gente. (The avenue is full of people.)
2. Sabes onde fica a avenida principal? (Do you know where the main avenue is?)
3. Gosto de conduzir por esta avenida à noite. (I like driving along this avenue at night.)
4. Há muitas árvores nesta avenida. (There are many trees on this avenue.)
5. A avenida é muito ruidosa durante o dia. (The avenue is very noisy during the day.)