"My generation does not eat fish."
Translation:Minha geração não come peixe.
They mean the same in this context. There are times when prefixing possessives like "meu(s)/minha(s)/seu(s)/sua(s)/nosso(s)/nossa(s)" with the definite articles "o(s)/a(s)" is not natural, but it is simply optional in most cases. For a lot more about the exceptions see Ruama's comments here: