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

Yes

The spelling, meaning, and grammatical function of "sinceramente" are identical in both Brazilian and Continental Portuguese. The only difference lies in pronunciation. In Brazilian Portuguese, the vowels are more open and the unstressed final "e" is often pronounced as a light "i" sound. In Continental Portuguese, the pronunciation is much more closed; unstressed vowels are frequently reduced or nearly silent, making the word sound more clipped and compressed.

Brazilian Portuguese

1. Sinceramente, eu não gosto de viajar de ônibus. (Honestly, I don't like traveling by bus.)
2. Sinceramente, acho que esse filme é muito legal. (Honestly, I think this movie is very cool.)
3. Sinceramente, eu não sei o que dizer. (Honestly, I don't know what to say.)
4. Sinceramente, ele foi muito gentil comigo. (Honestly, he was very kind to me.)
5. Sinceramente, você está sendo muito chato. (Honestly, you are being very annoying.)

Portuguese (Continental)

1. Sinceramente, não gosto de viajar de autocarro. (Honestly, I don't like traveling by bus.)
2. Sinceramente, acho que este filme é muito porreiro. (Honestly, I think this movie is very cool.)
3. Sinceramente, não faço ideia do que dizer. (Honestly, I have no idea what to say.)
4. Sinceramente, ele foi muito simpático comigo. (Honestly, he was very nice to me.)
5. Sinceramente, estás a ser uma seca. (Honestly, you are being a bore.)