It is not clear whether the guilty feeling of indulging in a knowingly unethical practice of forbidden moonlighting or the fear of being caught prompted the anonymous friend to raise this question. Whatever it may be, it is now clear that he is not faithful and honest to both employers. In case he successfully resigns from his present regular job, which might be of relative insignificance, to pursue the traineeship in the other better organization, what is the guarantee that the prospective employer would take it lightly if his dual employment comes to light later? Efficiency, effectiveness, etc., are relative in the realm of employment, whereas honesty is an absolute trait of a person seeking employment under someone else for his livelihood.
The poster should remember the proverb: "A bird in the hand is worth two in the bush!"