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

No

In Brazilian Portuguese, fazenda almost exclusively refers to a large farm, plantation, or rural estate used for agriculture or livestock. In Continental Portuguese, while the word can technically refer to a farm in a literal sense, it is much more commonly associated with a clothing store or the fabrics/textiles themselves (similar to "haberdashery" or "fabric shop"). To express the idea of a farm or a rural estate, a person from Portugal would naturally use the word quinta.

Brazilian Portuguese Examples (using fazenda as "farm")

1. Eu nasci em uma fazenda de gado. (I was born on a cattle farm.)
2. A fazenda é muito longe da cidade. (The farm is very far from the city.)
3. Eles estão construindo uma nova fazenda. (They are building a new farm.)
4. A fazenda produz milho e soja. (The farm produces corn and soy.)
5. Minha família tem uma fazenda no interior. (My family has a farm in the countryside.)

Continental Portuguese Examples (using quinta to express the same idea)

1. Eu nasci numa quinta de gado. (I was born on a cattle farm.)
2. A quinta é muito longe da cidade. (The farm is very far from the city.)
3. Eles estão a construir uma nova quinta. (They are building a new farm.)
4. A quinta produz milho e soja. (The farm produces corn and soy.)
5. A minha família tem uma quinta no interior. (My family has a farm in the countryside.)