Are the cables now routed internally through the new handlebars? If so it may be the housing/cable may be at a harsher angle causing just enough friction to restrict smooth shifting.
I had this problem with me new Enve h'bars. They allow for internal routing but the angle is so harsh they just didn't allow for smooth shifting. I just placed the housings under the bars and the problem is solved. Shifting is smooth and fast as always.
It is never a bad idea to replace cables/housings periodically...make sure you have smooth arcs for fast and smooth shifting.
Good luck and keep us informed.