Not all kevlar tires are created equally. I had a set of tires that had a belt down the middle. I kept getting flats on the side or just off the middle. I ended up getting Armadillos which have a larger kevlar belt. That bike has not had a flat since.

That being said, if you like the tires on that bike, try the liners. It really does depend on where you live (thorns) and where you are going to ride (glass). The liners may work beautifully for you.