There's little to gain and much to lose by responding directly to online comments. For one thing, you have to be extraordinarily disciplined to avoid responding emotionally to criticism. For another, there are large pools of people who have raised to an artform the skill of drawing people into arguments (and goading them into making unwise responses they can then mock them mercilessly for).
As someone who has achieved the not-inconsiderable goal of publication in mainstream press, you have a loftier platform than the comments section. In general, I would stick to your platform, and leave them to theirs --after all, you don't want to risk a reputation that I'm sure took you a lot of time and effort to build.
There are, of course, some people who excel at interacting directly with their fans, and this can be a way for them to build a larger, more loyal audience, but if you want to go this route, make sure you go in with your eyes open. My best advice would be to put the same level of care, polish and professionalism into your comments as into your articles. Never be fooled into thinking you're in a private conversation.