A SSD has 10X faster access time and 5X faster transfer rate but costs 10X as much per GB.
Both have their uses. SSDs are fast, HDDs have much lower cost per byte.
There isn't much else to it. You can add that SSDs have no mechanical parts so they are more vibration-resistant than HDDs but that is usually not a problem for desktop PCs and rarely a major concern with laptops since nobody plans to drop their laptops on a regular basis either.
Even an entry level SSD is insanely fast (that's a technical term) compared to a HDD. After I got my first one, I added one to my other two machines because it's just that much better.
Only thing I'd ever put on a HDD are photos, movies, music, docs.