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

Yes

The word "muita" is identical in meaning, spelling, and grammatical function in both Brazilian and Continental Portuguese. The only difference is pronunciation. In Brazilian Portuguese, the vowels are generally more open and clearly articulated. In Portugal, unstressed vowels are often "reduced" or "closed," which makes the "u" in "muita" sound much shorter, almost as if it were swallowed or neutralized.

Brazilian Portuguese Examples:

1. Tem muita gente na festa. (There are a lot of people at the party.)
2. Tem muita comida na mesa. (There is a lot of food on the table.)
3. Ela está fazendo muita coisa hoje. (She is doing a lot of things today.)
4. Tem muita poeira nesse quarto. (There is a lot of dust in this room.)
5. Você tem muita sorte. (You are very lucky.)

Portuguese (Continental) Examples:

1. Há muita gente na festa. (There are a lot of people at the party.)
2. Há muita comida na mesa. (There is a lot of food on the table.)
3. Ela está a fazer muita coisa hoje. (She is doing a lot of things today.)
4. Há muita poeira neste quarto. (There is a lot of dust in this room.)
5. Tens muita sorte. (You are very lucky.)