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

Yes

The meaning, spelling, and grammar of the word "batatas" are identical in both Brazilian and Continental Portuguese. The only difference lies in pronunciation. In Brazilian Portuguese, the vowels tend to be more "open" and the rhythm is more melodic and syllable-timed. In Continental Portuguese, unstressed vowels (especially the final "a") are often more "closed" or even reduced, and the rhythmic stress of the word differs.

Brazilian Portuguese

1. Eu adoro comer batatas fritas. (I love eating french fries.)
2. As batatas estão muito gostosas. (The potatoes are very tasty.)
3. Você prefere batata cozida ou assada? (Do you prefer boiled or roasted potatoes?)
4. Eu vou fazer um purê de batata. (I am going to make mashed potatoes.)
5. Comprei um quilo de batatas no mercado. (I bought a kilo of potatoes at the market.)

Continental Portuguese

1. Estou a comer batatas fritas. (I am eating french fries.)
2. As batatas estão muito boas. (The potatoes are very good.)
3. Gostavas de comer batata cozida? (Would you like to eat boiled potatoes?)
4. Vou fazer puré de batata. (I am going to make mashed potatoes.)
5. Comprei um quilo de batatas no mercado. (I bought a kilo of potatoes at the market.)