I'm not familiar with any internal comparisons/tests for SSDs vs non-SSDs.
However in theory, I expect there to actually be very minimal (if any) performance gains by switching the PI Web API to an SSD.
Once the DLLs are loaded from disk into memory by the process (on Service Startup), the majority of all processing is done in-memory or via AFSDK network calls, and very little data is committed to disk or read from disk.
The only Disk IO I can think of off the top of my head would be logging to the Windows Event Logs.
If you are performing this upgrade because you have current performance concerns or issues with the PI Web API, we'd be interested to hear about those so that we can troubleshoot them, but I would expect minimal tangible benefits for the PI Web API specifically from switching to an SSD.