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

No

While the core dictionary definitions of "conveniente" are identical in both varieties (meaning appropriate, opportune, or advantageous), there is a difference in typical usage.

In Brazil, "conveniente" is primarily used to describe things that are socially, ethically, or professionally "appropriate" or "advantageous." When a Brazilian wants to express that something is "handy," "easy to use," or "user-friendly" (the English concept of "convenient"), they much more naturally use the word "prático". In Portugal, "conveniente" is used more broadly and is the standard word for both "appropriate" and "handy/easy to access."

Brazilian Portuguese Examples

1. Não é conveniente falar sobre esse assunto agora. (It is not appropriate to talk about this subject right now.)
2. O metrô é muito prático para o dia a dia. (The subway is very practical/handy for daily life.)
3. Escolha o horário que for mais conveniente para você. (Choose the time that is most convenient/appropriate for you.)
4. Achei esse jeito de viajar muito prático. (I found this way of traveling very practical/handy.)
5. Ele só faz o que é conveniente para ele. (He only does what is advantageous/convenient for him.)

European Portuguese Examples

1. Não é conveniente falar sobre este assunto agora. (It is not appropriate to talk about this subject right now.)
2. O metro é muito conveniente para o quotidiano. (The subway is very convenient/handy for daily life.)
3. Escolha o horário que for mais conveniente para si. (Choose the time that is most convenient/appropriate for you.)
4. Achei esta forma de viajar muito conveniente. (I found this way of traveling very convenient/handy.)
5. Ele só faz o que é conveniente para ele. (He only does what is advantageous/convenient for him.)