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

Yes

The word "sugiro" (the first-person singular present indicative of the verb sugerir) is identical in meaning, spelling, and grammatical function in both Brazilian and Continental Portuguese. The only difference is pronunciation. In Brazilian Portuguese, the vowels are generally more open and the rhythm is more "syllable-timed," meaning each syllable receives a more distinct weight. In Continental Portuguese, unstressed vowels (like the "u" and the "o" in sugiro) are often more closed or even reduced/devoiced, making the word sound shorter and more "clipped" to a Brazilian ear.

Brazilian Portuguese Examples

1. Sugiro que a gente vá ao shopping. (I suggest we go to the mall.)
2. Eu sugiro que você tente de novo. (I suggest that you try again.)
3. Sugiro pegar um táxi para não se atrasar. (I suggest taking a taxi so you aren't late.)
4. Sugiro esse restaurante, é muito bom. (I suggest this restaurant, it's very good.)
5. Sugiro a gente estudar um pouco mais. (I suggest we study a bit more.)

Continental Portuguese Examples

1. Sugiro que vamos ao centro comercial. (I suggest we go to the shopping center.)
2. Sugiro que tu leias este livro. (I suggest that you read this book.)
3. Sugiro apanhar o autocarro. (I suggest taking the bus.)
4. Sugiro este restaurante para o jantar. (I suggest this restaurant for dinner.)
5. Sugiro-te que tenhas cuidado. (I suggest to you that you be careful.)