What would be the reason to administer antioxidants to broilers? If it is to protect certain nutrients in the feed eg fatty acids, than the feed is the obvious carrier to choose.

If you expect (general) health benefits for administering antioxidants, the water could be the carrier as well. But..... be aware that some chemicals are not easily mixed with water or that the solutions might not be stable.

Also the drinking system might not permit easy (long term) administration of additives. The organic material in the antioxidants  might also be a source of nutrients to micro organisms present and growing in the drinking system.

Regular cleaning might become imperative!

Depends on the type, source and concentrations of antioxidants. Generally, feed would be more appropriate. 

Here in Macedonia we are still using YU standards (Yugoslavian standards) where all vitamins, antibiotics micro-elements we put into the water which is usually drinking water

Best

The chemical composition of most antioxidant make feed the preferable medium of administration except the producer has consider water solubility..Yes YU standards recommend drinking water but the producer will produce specifically for that standard 

Vitamin C is the only product I can think of that has some antioxidant properties and is administered in the water. Everything I've worked with has been in the feed. I feel you can more accurately control the dose with feed. Adding it to the feed also provides oxidative stability to feed ingredients that might otherwise be succeptible to oxidative damage. 

Feed is more acceptable for such additives