I assume that you are referring to the news article Onion based preservatives from 17th April this year
In general antioxidants are not heat-resistant but will break down at different levels of heat, something observed in a study found in the Journal of Science in Food and Agriculture, November 2003. Broccoli cooked at max heat for 5 minutes had a great loss of antioxidants, at the same time heat will actually increase antioxidant content of some foods such as tomatoes and carrots. Both the food, temperature, cooking method and cooking time affects the antioxidant level of the food.
To answer your question, whether onions display the same antioxidant activity level after cooking, it depends on cooking time and method. According to the study Cooking Loss of Major Onion Antioxidants and the Comparison of Onion Soups Prepared in Different Ways simple boiling and oven baking at 100C resulted in little loss of antioxidant activity, but antioxidant activity was considerably degraded at 200C (oven baking).
With kind regards Iris Daniela Classon