Gunpowder made ancient and medieval walls obsolete. Period. End of story. First of all, they were simply too thin -- and nobody over-built them in anticipation of cannons being invented.
-- HOWEVER, with other advancements in construction, you have the introduction of star-shaped citadels etc. whose origination is mainly associated with the French military engineer Vauban. It was against such walls that the English and French had such fun at Sevastopol during the Crimean War. Indeed, the epitome of the "Vauban Wall" was Verdun or one of its WWI contemporaries -- nice thick walls (although ultimately vulnerable to the very-limited availabilty Krupps 240mm seige guns, as amply demonstrated in Belgium in 1914), sophisticated overlapping fields of fire, etc.
So, two types of walls -- "ancient" and "Vauban".
Besiegingly Yours,
Oz