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

Yes

The spelling, meaning, and grammatical gender of "manjericão" are identical in both Brazilian and Continental Portuguese. The only difference is in pronunciation. In Brazilian Portuguese, the vowels are more open and the articulation is more distinct; for example, the final "o" is clearly pronounced as a "u" sound. In Continental Portuguese, vowels—especially unstressed ones—are much more closed and "swallowed," making the word sound shorter and more clipped.

Brazilian Portuguese Examples

1. Eu adoro colocar manjericão na pizza. (I love putting basil on pizza.)
2. Você comprou manjericão no mercado hoje? (Did you buy basil at the market today?)
3. O cheiro de manjericão fresco é maravilhoso. (The smell of fresh basil is wonderful.)
4. Eu estou fazendo um molho de manjericão para o macarrão. (I am making a basil sauce for the pasta.)
5. Tem muito manjericão nesta salada. (There is a lot of basil in this salad.)

Continental Portuguese Examples

1. Adoro pôr manjericão na pizza. (I love putting basil on pizza.)
2. Compraste manjericão no mercado hoje? (Did you buy basil at the market today?)
3. O cheiro de manjericão fresco é maravilhoso. (The smell of fresh basil is wonderful.)
4. Estou a fazer um molho de manjericão para a massa. (I am making a basil sauce for the pasta.)
5. Há muito manjericão nesta salada. (There is a lot of basil in this salad.)