Daan's answer is pointing to Eric Hammond's excellent summary of all EBS benefits already (+1), but to stress one point again upfront:
Ephemeral storage will be lost on stop/start cycles and can generally go away, so you definitely don't want to put anything of lasting value there, i.e. only put temporary data there you can afford to lose or rebuild easily, like a swap file or strictly temporary data in use during computations. Of course you might store huge indexes there for example, but must be prepared to rebuild these after the storage has been cleared for whatever reason (instance reboot, hardware failure, ...).
So storing a MySQL database on ephemeral storage isn't a good idea in the first place, except if you exactly know what you are doing and are prepared to always have point in time backups etc.
That said, this indeed belongs to Server Fault, and there have been quite some similar or related questions asked and answered already - I usually don't link to a search result, but that's actually helpful here, see ebs ephemeral performance; the answers I consider most relevant for an ad hoc judgement are:
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