Taking into account purely functional considerations, I always build wooden walls as a just-in-case measure to give me time to rush a field army to my settlement's defence in the event of a surprise attack - something more likely now that rebels are more aggresive.
If the local enemy or neutral factions are fielding elephants and/or siege engines then I'd consider upgrading to stone walls but it would depend on the value of the city - and I might highly value a city simply for the temple it holds, for example, or because it's in a strategic location, not just monetary terms or troop building capability.
On rare occasions I like to build up the defences of a city because I know an enemy faction will keep trying to take it and it's a great way to weaken them by getting them to break their teeth as they try to storm the city or counter a sally.
(I'm currently having fun in my latest Julii campaign doing this to the Carthaginians and Greeks on Sicilly: with some help from my agents the Scipii are gone and I managed to acquire Messana, although the damned Brutii beat me to Capua due to the sheer luck of having an army marching past at the time. :( My main armies are busy in northern europe, but with a new general and some veteran troops I'd luckily just sent back from the front for retraining to the latest upgrades I'm able to tie up both factions until I'm free to crush them.)
Eventually I like to upgrade all my cities to stone walls, but that's simply because I don't like the image of them being protected by some scrappy wooden fence. By the time I get around to this I'm usually flush with cash and it doesn't really matter that I'm 'wasting' money.
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