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

No.

While the dictionary definition and spelling of "tigela" are identical in both dialects, there is a difference in typical usage. In Brazil, "tigela" is the standard, generic term for almost any deep, round dish, whether it is used for cereal, soup, fruit, or mixing ingredients. In Portugal, "taça" is the much more natural and frequent word for small, individual-sized bowls (such as those used for yogurt, cereal, or dessert). In Portugal, the word "tigela" is typically reserved for larger, deeper, or more utilitarian vessels, such as a mixing bowl.

Brazilian Portuguese

1. Eu coloquei o cereal na tigela. (I put the cereal in the bowl.)
2. A tigela de plástico é muito útil. (The plastic bowl is very useful.)
3. Use uma tigela grande para bater a massa. (Use a large bowl to beat the dough.)
4. Ele serviu a sopa em uma tigela pequena. (He served the soup in a small bowl.)
5. A tigela estava cheia de frutas. (The bowl was full of fruit.)

Continental Portuguese

1. Eu coloquei os cereais na taça. (I put the cereal in the bowl.)
2. A taça de plástico é muito útil. (The plastic bowl is very useful.)
3. Usa uma tigela grande para bater a massa. (Use a large bowl to beat the dough.)
4. Ele serviu a sopa numa taça pequena. (He served the soup in a small bowl.)
5. A taça estava cheia de fruta. (The bowl was full of fruit.)