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

No.

While the spelling and fundamental meaning of "protege" are identical in both dialects, there are significant differences in grammar and typical usage:

1. Grammar (Clitic Placement): In Brazilian Portuguese, it is standard to use proclisis, where the object pronoun precedes the verb (e.g., "Ele me protege"). In Continental Portuguese, the standard is enclisis, where the pronoun follows the verb (e.g., "Ele protege-me").
2. Pronunciation: Brazilian Portuguese features more open vowels and a syllabic rhythm. In contrast, Continental Portuguese features more closed or even reduced (nearly silent) unstressed vowels and follows a stress-timed rhythm.

Brazilian Portuguese Examples:

1. Ele me protege. (He protects me.)
2. O seguro protege o carro. (The insurance protects the car.)
3. Isso te protege do frio. (This protects you from the cold.)
4. A lei protege os trabalhadores. (The law protects the workers.)
5. Ela protege a criança. (She protects the child.)

Continental Portuguese Examples:

1. Ele protege-me. (He protects me.)
2. O seguro protege o automóvel. (The insurance protects the automobile.)
3. Isso protege-te do frio. (This protects you from the cold.)
4. A lei protege os trabalhadores. (The law protects the workers.)
5. Ela protege a criança. (She protects the child.)