Use To Sphere tool. After adding the vertical loop cuts select each loop with Alt+RMB, change the pivot type to Individual Origins, press Shift+Alt+S and drag the cursor outwards the mesh. Select the other loop and press Shift+R to repeat the process. Do the same with the other ones. Now you've got additional loops in your mesh and it's also perfectly smooth.
EDIT: If you need to add the horizontal loopcuts also you may subdivide your mesh (W-->Subdivide), then smooth the vertices (Ctrl+V-->Smooth Vertex) and increse the Smoothing value to 1.000. As you can see the objects look the same.