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

Yes

The word "inseto" is identical in spelling, meaning, and grammatical function in both Brazilian and Continental Portuguese. The only differences are phonetic. In Brazil, the vowels are typically more open and clearly articulated, and the "s" is usually pronounced as a soft /s/. In Portugal, the vowels are much more "closed" or reduced (sometimes almost disappearing), and the "s" at the end of a syllable is pronounced as a "sh" sound (/ʃ/).

Brazilian Portuguese Examples

1. Vi um inseto estranho no jardim. (I saw a strange insect in the garden.)
2. Esse inseto está picando meu braço. (This insect is biting my arm.)
3. Tem muito inseto aqui em casa. (There are many insects here at my house.)
4. Eu odeio insetos voadores. (I hate flying insects.)
5. O repelente ajuda a afastar os insetos. (The repellent helps to keep insects away.)

Continental Portuguese Examples

1. Vi um inseto esquisito no jardim. (I saw a strange insect in the garden.)
2. Este inseto está a picar-me o braço. (This insect is biting my arm.)
3. Há muitos insetos durante o verão. (There are many insects during the summer.)
4. Detesto insetos voadores. (I hate flying insects.)
5. O repelente serve para afastar os insetos. (The repellent serves to keep insects away.)