You can make Postgres scale, but there is an operational cost to it. DynamoDB does that for you out of the box. (So does Aurora, to be honest, but there is also an overhead to setting up an Aurora cluster to the needs of your business.)
I've found also that in Postgres the query performance does not keep up with bursts of traffic -- you need to overprovision your db servers to cope with the highest traffic days. DynamoDB, in contrast, scales instantly. (It's a bit more complicated that that, but the effect of it is nearly instantaneous.) And what's really great about DynamoDB is after the traffic levels go down, it does not scale down your table and maintains it at the same capacity at no additional cost to you, so if you receive a burst of traffic at the same throughput, you can handle it even faster.
DynamoDB does a lot of magic under the hood, as well. My favorite is auto-sharding, i.e. it automatically moves your hot keys around so the demand is evenly distributed across your table.
So DynamoDB is pretty great. But to get the the best experience from DynamoDB, you need to have a stable codebase, and design your tables around your access patterns. Because joining two tables isn't fun.