I do both and still can't get my nitrates to stay up :-/
Using a food will give many nutrients, whereas KNO3 will only give you K and NO3. Nitrates are rarely an issue as they should be incredibly low anyways and feeding usually introduces those. I do find feeding coral food increases polyp extension, but there is one huge downside to coral foods.... vermetids..... they love that size of partical and if they stay well fed, your tank will be covered in snot webs that will actually irritate your corals.
I think if your issue is low nitrates, I would go the KNO3 route just because it's cleaner and more accurate dosing from a chemistry standpoint. (Make your solution to a concentration that will raise your nitrates by .25 per 5 mL or so and you'll have great control.)
Also, I would use lab grade KNO3 if you do it. I know a lot of people use the spectracide stump remover, but purity goes a long ways in this hobby and lab grade compounds have regulations. Stump remover has much less strict purity requirements. (Although this part is a personal preference and largely a peace of mind thing. I prefer to be confident I'm not adding anything unwanted to the system. Plus even the lab grade stuff is pretty cheap, so why chance it.)