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

No

While the spelling and grammar of "bife" are identical in both dialects, there is a difference in typical usage. In Brazilian Portuguese, "bife" almost exclusively refers to a thin slice of meat that has been pan-fried (similar to a cutlet). In Portugal, the term is much broader and is frequently used to describe much thicker, more substantial cuts of meat (similar to what an English speaker would call a "steak").

Brazilian Portuguese Examples

1. Eu gosto de comer bife acebolado no almoço. (I like to eat steak with onions for lunch.)
2. O bife de alcatra está muito suculento. (The sirloin steak is very juicy.)
3. Você prefere o bife malpassado ou bem passado? (Do you prefer the steak rare or well-done?)
4. Vou fritar um bife rápido para o jantar. (I'm going to fry a quick steak for dinner.)
5. Esse bife de contrafilé é o meu favorito. (This strip steak is my favorite.)

Portuguese Examples

1. Gostaria de pedir um bife de lombo. (I would like to order a loin steak.)
2. O bife está demasiado cozido. (The steak is overcooked.)
3. O bife à portuguesa é um prato muito tradicional. (Portuguese-style steak is a very traditional dish.)
4. Queria um bife acompanhado de batatas fritas. (I would like a steak accompanied by french fries.)
5. Este bife de vaca é excelente. (This beef steak is excellent.)