I am not an expert on this subject. But I will tell you what I think I know (for what little it's worth).
SSDs do fail, but for different reasons that HDDs. I would definitely backup my music even if stored on a SSD.
The big advantage that SSDs have over HDDs is faster access time, which is great to improve bootup time. The boot time on my B2 is about 10 seconds. Also, the OS is stored on the SD card, not the HDD. So having an SDD will not have any effect on boot time.
When I select a song to play, it takes probably less than a second to start playing. It's fast enough that I've never tried to time it. With an SDD, that already short access time would be shorter, but I doubt I would notice. Once the song has started to play, either type of drive can keep up with the demand without any problem.
SSD is solid state and has no mechanical moving parts. So in the case where it is dropped, it would be less likely to lose data.
Do a Google search for "Is SSD more reliable than HDD?" and you'll get more information.