It has been a while since I looked into solid state, but I will give you my experience based upon the device drivers I wrote years ago.
Generally, it depends upon the hardware, the I/O channels, and the software driver. Just as there are slower hard drives there are slower solid state drives.
Back in my device driver days, back when Digital was king, the solid state drives did not suffer from the standard latencies that standard hard drives would have to contend with. This would include the spin rate of the platter, the speed of the arm, the sensitivity of the read/write head, the size of the cache, the internal driver, and so on. For a solid state drive, most all of these considerations disappear. The memory used in solid state drives, at the time anyway, were not always the fastest available. While some were extremely fast, these cost quite a bit more. There was a heavy dependency upon the engineering of the on-board bus system and the supporting components that dictated speed. However with solid state, the I/O rate stayed consistent and did not need optimization to recover seek and read times. Finally, solid state did not generally crash.
Today, if I were buying a server, I would be looking at solid state. But I caution you to buy the best you can. They can be much faster and much more reliable.
To answer your question, I would be asking what drives the ISP uses so that you can look at seek and read times (research online) as well as ask what I/O channels they are such as SCSI, Fiber, SATA, and so on. Back when I was buying servers for my webhost business, I preferred SCSI 3 which is a very fast and reliable standard. It may be that your ISP is using SAN which mitigates most of your concerns due to striping, fibre, and fail-over. If they are using SAN, it really does not matter if the HD is solid state or not. Not to you anyway.