Is it actual sway (as in, you can see the trailer's back end going back & forth) or is it "wind wag", where the trailer itself seems to be slightly rocking back & forth? Wind wag is pretty common and something you usually can get used to. Could be your hitch needs some adjusting. If it's sway, then yes, the sway bar should be doing a better job.
We tow with an Equal-i-zer, which has two rigid sway bars which use friction against brackets on the tongue, rather than being attached by chains. Have not had a problem with sway, even when towing our previous 34' TT (and in pretty windy conditions; if sustained winds are over 35 mph we usually try not to travel.