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

Yes.

The word "ultimamente" 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 clearly articulated. In Continental Portuguese, unstressed vowels (such as the "e" in the middle of the word) are often significantly reduced or nearly silent, making the word sound more "compressed."

Brazilian Portuguese

1. Eu tenho trabalhado muito ultimamente. (I have been working a lot lately.)
2. Ultimamente, eu não tenho dormido bem. (Lately, I haven't been sleeping well.)
3. O que você tem feito ultimamente? (What have you been doing lately?)
4. Ele parece meio triste ultimamente. (He seems a bit sad lately.)
5. As coisas estão bem difíceis ultimamente. (Things have been quite difficult lately.)

Continental Portuguese

1. Tenho trabalhado muito nos últimos tempos. (I have been working a lot lately.)
2. Ultimamente, não tenho conseguido descansar. (Lately, I haven't been able to rest.)
3. O que tens feito ultimamente? (What have you been doing lately?)
4. Recentemente, ele tem estado muito ocupado. (Recently, he has been very busy.)
5. As coisas têm estado complicadas nos últimos tempos. (Things have been complicated lately.)