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

Yes

The spelling, meaning, and grammatical function of the word are identical in both dialects. The only difference is the pronunciation of the final unstressed vowel: in Brazilian Portuguese, the "e" is typically pronounced as a light "i" (/suˈspẽsi/), whereas in European Portuguese, it is a more closed, neutral vowel (/susˈpẽsu/).

Brazilian Portuguese Examples

1. O filme era puro suspense. (The movie was pure suspense.)
2. Não aguento mais esse suspense! (I can't stand this suspense anymore!)
3. O final me deixou em suspense. (The ending left me in suspense.)
4. Adoro histórias de suspense. (I love suspense stories.)
5. A notícia deixou todo mundo em suspense. (The news left everyone in suspense.)

European Portuguese Examples

1. O filme era puro suspense. (The movie was pure suspense.)
2. Já não aguento este suspense! (I can't stand this suspense anymore!)
3. O final deixou-me em suspense. (The ending left me in suspense.)
4. Adoro histórias de suspense. (I love suspense stories.)
5. A notícia deixou toda a gente em suspense. (The news left everyone in suspense.)