Dual Intel Xeon E5-2670 (current) vs AMD Ryzen 9 3900 (new box), for combined web/database server

There are a very few server motherboards out there with proper IPMI/BMC, ECC RAM support, etc., that will support Ryzen. But they are few and far between. Except for support for ECC memory, AMD doesn't provide much support for Ryzen in servers (yet). That said, if you're very cost sensitive, you have proper out of band remote access to the machine, and can live with the memory limit, it can work. The big thing that concerns me here is that your NVMe drives are probably not hot swappable. When one fails you'll have some downtime while it is physically replaced. Again, if you can live with that...

That all said, yes, the Ryzen will absolutely destroy your current server in terms of raw performance.

I would never use a consumer desktop CPU in a professional environment, for one they're very memorylimited, they don't have RAS features and aren't designed to maintain the uptime of a server-class CPU, see if you can get hold of an EPYC-based server. Also PLEASE don't use R5, especially with >1TB disks, it's dangerous and essentially negligent - R1/10, R6/60 and ZFS are the only games in town.