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

No.

While the spelling and the grammatical conjugation of "teve" (the third-person singular of the verb ter) are identical in both dialects, there is a significant difference in typical usage. In Brazil, "teve" is frequently used in colloquial speech as an existential verb to mean "there was" or "there were." In Portugal, using "ter" to express existence is generally considered grammatically incorrect or very informal; a Portuguese person will naturally use the verb haver (specifically houve in the past tense) to express that something occurred or existed.

Brazilian Portuguese Examples

1. Teve um problema no celular. (There was a problem with the cell phone.)
2. Ele teve muita sorte. (He was very lucky.)
3. Teve muita gente na festa. (There were many people at the party.)
4. Você teve tempo de estudar? (Did you have time to study?)
5. Teve um acidente na avenida. (There was an accident on the avenue.)

Portuguese (Portugal) Examples

1. Houve um problema no telemóvel. (There was a problem with the mobile phone.)
2. Ele teve muita sorte. (He was very lucky.)
3. Houve muita gente na festa. (There were many people at the party.)
4. Tu tiveste tempo de estudar? (Did you have time to study?)
5. Houve um acidente na avenida. (There was an accident on the avenue.)