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

No.

While the fundamental meanings of "pronto" (ready, finished, or prompt) are identical in both dialects, there is a difference in typical usage regarding its function as a conversational filler or interjection. In Brazilian Portuguese, "pronto" is a versatile "catch-all" interjection used to signal the completion of a task, to mark a transition between topics (similar to "anyway" or "so"), or to conclude a point (similar to "there" or "there you go"). While "pronto" is also used in Continental Portuguese, speakers there more frequently rely on "já está" to signal that a task is finished, and "bem" or "pois" to handle conversational transitions or acknowledgments.

Brazilian Portuguese Examples

1. Pronto, terminei o trabalho. (There, I finished the work.)
2. Pronto, agora vamos sair. (Anyway, now let's go out.)
3. Pronto, você tem razão. (There, you are right.)
4. O almoço está pronto. (Lunch is ready.)
5. Pronto, eu vou. (Okay, I'm going.)

Continental Portuguese Examples

1. Já está, terminei o trabalho. (It's done, I finished the work.)
2. Bem, agora vamos sair. (Well, now let's go out.)
3. Pois, tens razão. (Indeed, you are right.)
4. O almoço está feito. (Lunch is done.)
5. Está bem, eu vou. (Alright, I'm going.)