I mean ultimately SATA and NVMe are just an interconnect. The biggest difference is throughout. Yes there can be some minor latency or round trip gains in the protocol but throughout is the biggest difference.
Lower confidence: I think there's also a latency differences due to better control over interrupts with NVMe than SATA. Especially on a multi socket system, or even a higher core count single CPU system, that's quite a win.
There's prominent references to needing just one MMIO write for NVMe command submission in the NVMe spec:
"Does not require uncacheable / MMIO register reads in the command submission or completion path.
A maximum of one MMIO register write is necessary in the command submission path."
Page 7 of https://nvmexpress.org/wp-content/uploads/NVM-Express-1_4b-2...
I didn't quickly re-find the relevant SATA/AHCI spec parts, but there's some references in other places, e.g. https://spdk.io/news/2019/05/06/nvme/ :
"The NVMe specification is designed to significantly reduce the number of required MMIO compared to older specifications like AHCI. AHCI requires as many as 7 total MMIO operations (many of which are reads) per I/O, whereas NVMe requires an MMIO write only to ring the doorbell both on the submission and completion side. MMIO writes are posted, meaning the CPU does not stall waiting for any acknowledgement that the write made it to the PCIe device. This means that MMIO writes are much faster than MMIO reads. That said, they still have a significant cost."
And even that one doorbell write (for each of submission and completion) can be batched.
I'm not sure why I remember three - that might just have been the average number in simple scenarios, rather than the max.