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

Yes

The spelling, meaning, and grammatical function of the word "modelo" are identical in both Brazilian and Continental Portuguese. The only difference is in pronunciation. In Brazilian Portuguese, the vowels are more "open" and the syllables are clearly articulated (e.g., the "e" sounds like the "e" in "met"). In Continental Portuguese, there is significant vowel reduction; the unstressed "e" becomes much more closed (sounding almost like a muffled "i" or nearly silent), and the "o" is also more compressed.

Brazilian Portuguese examples:

1. Este modelo de carro é muito econômico. (This car model is very economical.)
2. Ela trabalha como modelo profissional. (She works as a professional model.)
3. Você precisa baixar este modelo de documento. (You need to download this document template.)
4. O novo modelo do celular é incrível. (The new cell phone model is amazing.)
5. Ele é um modelo de bom comportamento. (He is a model of good behavior.)

Continental Portuguese examples:

1. Este modelo de carro é muito económico. (This car model is very economical.)
2. Ela trabalha como modelo profissional. (She works as a professional model.)
3. Precisas de descarregar este modelo de documento. (You need to download this document template.)
4. O novo modelo do telemóvel é incrível. (The new mobile phone model is amazing.)
5. Ele é um modelo de bom comportamento. (He is a model of good behavior.)