AON Networks are P2P, no not THAT P2P but Point-to-Point so each user theoretically has their own dedicated fibre strand terminated to a concentrator, and AON networks generally have amplifiers, repeaters and shaping circuits, but naturally there are far more points that require powered devices, so more points of failure should there be power outages with inadequate power backup, or from acts of god if they are not protected properly etc.
PON Networks are P2MP or PTMP, and generally use passive components and optical splitters that split to 32 or 64 ONTs in batches of 4, but it can max at 128 with the right equipment and bandwidth, and/or bandwidth control. However portions of the network use shared fibre, not the entire thing.
The advantages of AON are simple. You have a dedicated line with the bandwidth from the port also being dedicated i.e. no sharing, meaning higher speeds and bandwidth are more possible and fault finding is also far easier. However AON systems are inherently more expensive to deploy due to the higher requirement for powered active equipment. The advantages of PON might not seem like advantages but the TCO is lower, installation costs and rollout costs are lower, maintenance costs are lower, and there are fewer points of failure due to not having so many active components in the network. It does make fault finding more difficult due to the shared nature of PON, but it allows for a less complex rollout which takes less time, and offers users a far more palatable price point for their internet.
However both are perfectly feasible topologies and I believe most of the networks in SA are PON based with a few AON based ones. AON tends to be used more for business and PON tends to be used more for home. If the networks here were more AON than PON I think the prices would be a lot higher. The PON networks work perfectly as long as the companies deploying them use them correctly and they don't let things get oversubscribed.
There are a few really good articles that explain the differences better than I can, and I only know what I know from a LOT of reading while patiently waiting for somebody to deem the areas I have lived in worthy of their time to put fibre in.