SSD has these main advantages:
Better performance.
Websites should not take more than 3 seconds to load and faster read/write speeds allow websites to load faster. SSDs can help to achieve this speed as the performance of SSD is much better than traditional hard drives.
Reliability.
SSD don't wear out over time as they don't have any moving parts and are more reliable than non-SSD drives. Traditional hard drives also good and reliable but SSDs use a more efficient technology that can stand better over time.
Environmentally friendly.
SSDs are more eco-friendly as they consume a lot less power compared to normal disks, produce no sound, and are cooler than HDDs.
While the disadvantages are:
More expensive.
Regarding prices per gigabyte, SSDs are more expensive than HDD.
Limited storage capacity. Although, it is getting better.
As compared to HDD, it stores less amount of data due to its low storage capacity.
Typically, SSD's are much faster. If you host uses CloudLinux, your IO limit would (hopefully) be larger than a host without SSD's.
SSD's are the future, and IMO, much better.