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

Yes.

The spelling, meaning, and grammatical function of "estátua" are identical in both Brazilian and European Portuguese. The only difference lies in pronunciation. In Brazilian Portuguese, the initial "e" is typically pronounced clearly, and the vowels are more open and melodic. In Continental (European) Portuguese, the initial "e" is often reduced to an [i] sound, and unstressed vowels (like the final "a") are much more closed or neutralized.

Brazilian Portuguese

1. A estátua do Cristo Redentor é maravilhosa. (The statue of Christ the Redeemer is wonderful.)
2. O menino ficou parado como uma estátua. (The boy stood still like a statue.)
3. Gostamos de ver a estátua de bronze na praça. (We liked seeing the bronze statue in the square.)
4. A estátua antiga está muito bem conservada. (The old statue is very well preserved.)
5. Ele colocou uma estátua pequena na estante. (He placed a small statue on the shelf.)

European Portuguese

1. A estátua do Cristo Redentor é fantástica. (The statue of Christ the Redeemer is fantastic.)
2. O rapaz ficou imóvel como uma estátua. (The boy remained motionless like a statue.)
3. Vimos uma estátua de bronze na praça. (We saw a bronze statue in the square.)
4. Aquela estátua antiga está muito bem conservada. (That old statue is very well preserved.)
5. Ele pôs uma estátua pequena na prateleira. (He put a small statue on the shelf.)