(Prices based on
https://calculator.aws/#/createCalculator and
https://www.hetzner.com/dedicated-rootserver?country=us)
An AuroraDB db.r5.xlarge with 10TB of storage, reserved instances 1Y term but no up-front, costs 1,301.40 USD per month.
Take a Hetzner AX161 with 4x3.84 TB SATA SSD, using RAIDZ for 11.52TB usable storage (and 4 times the RAM), at €297.00 per month... so 335.88 USD per month.
That's a difference of 965 $/mo = 11,580 $/yr. If you have 10 of these, they'll pay for a full time sysadmin. Now, that's leaving out a lot of details (bandwith costs and application hosting come to mind), and assumes truly massive databases. On the other hand, as that sysadmin, I promise our databases don't take anything like my full attention, and you really should have some sort of sysadmin/ops team anyways (please do not make devs run your AWS infrastructure; it will end in tears for everyone). Every time this argument comes up, people do mention reliability and time spent on maintenance, but... it's really not bad. Hardware doesn't actually fail that much, postgres isn't that complicated to configure, OS patches aren't that hard to apply. Your mileage will vary, but sometimes it's just not worth using AWS. (And sometimes, it really is; if we didn't need to run oversized databases, I'd push us to use AWS in a heartbeat)