Measuring the diameter of the rails is a good idea. If the new ones are smaller then the clamp probably is bottoming out.

What you need to do is 1st is look from the back of the saddle into the center area of the clamp where the bolt passes through. There should still be space between the top and bottom portions of the clamp. If not then the clamp is bottoming out before exerting full pressure on the rails. If that is the case you need to shim so that the clamp is forced apart more.

This is how I would make shims. I would call it shimming the clamp, but it comes to the same result. Remove the top bolt and clamp. Cut two narrow pieces of can twice as long as the clamp area on either side and about twice as wide. Be very careful with your fingers, as the pieces will be quite sharp. Fold each in 1/2 so that they are now the same length as the clamp area. Place each shim on the clamp and use a screwdriver shank to conform them to the curve of the clamp. Carefully place the saddle rails on top of the shims, replace the top portion of the clamp and the bolt, and tighten down the bolt.