According to sources like [this one](https://www.cs.utah.edu/~manua/pubs/systor15.pdf) NVMe SSDs can provide much greater sequential performance and up to 10X more IOPS than SATA SSDs.
For this reason, I have been checking into the VPS providers that say their storage is running on NVMe. Although obviously actual performance available for my VM depends on how much load the other VMs are putting on the storage, my guess is that starting from much better performance capability would result on significantly improved performance for the average customer (on an average day, if the costs work out to make the resource allocation equivalent or better).
There are a number of smaller VPS providers offering this, so I am considering giving one of those companies a chance the next time I need a VPS.
I noticed a few things that might be worth mentioning. One is that the actual performance can depend a lot on the driver used -- Virtio might be a good one. The other thing is that if you search for NVMe on Amazon you can find these PCIe cards that are like $3,000, which I think that means people may assume that NVMe refers to that.. which I think those cards and prices are outdated now with M.2/U.2-based systems and more mainstream deployment of these PCIe-based SSDs.
Here is an article that mentions M.2/NVMe in the data center: http://www.tomsitpro.com/articles/datacenter-m.2-ssd-pcie-specification,2-950.html