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

Yes

The word "com" is identical in meaning, grammar, spelling, and fundamental usage in both Brazilian and Continental Portuguese. The only difference lies in pronunciation. In Brazilian Portuguese, the nasal vowel is typically more open and clearly articulated. In Continental Portuguese, there is a stronger tendency toward vowel reduction, which can make the nasalized "o" sound much more closed or less prominent depending on the regional accent.

Brazilian Portuguese Examples

1. Eu gosto de café com leite. (I like coffee with milk.)
2. Eu vou ao shopping com meus amigos. (I am going to the mall with my friends.)
3. Ele falou com a professora. (He spoke with the teacher.)
4. Você quer comer com a gente? (Do you want to eat with us?)
5. Ele está com muita fome. (He is very hungry.)

Continental Portuguese Examples

1. Eu gosto de café com leite. (I like coffee with milk.)
2. Eu vou ao centro comercial com os meus amigos. (I am going to the shopping center with my friends.)
3. Ele falou com a professora. (He spoke with the teacher.)
4. Queres comer connosco? (Do you want to eat with us?)
5. Ele está com muita fome. (He is very hungry.)