It would be helpful to know a bit more of your game settings, the difficulty you're playing on in particular.
Next level walls mostly add more health - more hit points to the city that you need to chip away, and some limitations on the way to deal damage. As for the effectiveness of the bombardment, what's important here is the Combat Strenght (CS) difference between your siege CS and city defense CS, as in any other combat.
On lower difficulties, by the time you get to bombards, AI most probably haven't built more advanced and stronger land or sea units yet, which would bring up their city defensive CS to the next era level, so you bombard at a CS advantage, so all kind of walls just melt down.
On higer difficulties, AI tech quite fast and beeline to stronger melee units very soon, thus rendering their cities very strong, so you bombard their walls with your bombard corps and armies at CS parity at the best, or more probably at a disadvantage, because you're already bombarding with an obsolete siege unit in comparison to the advanced era defence they have, so the cannonballs just bounce off of any kind of walls. 1/15 off of Renaissance wall health sounds about right for bombarding at a slight CS disadvantage.