Ceramic: low ESR
Electrolytic: high ESR (relative to size)
Ceramics have the downside of tending to ring with nearby inductances. Putting in some ESR (in the right places) helps dampen that ringing.
The other downside of electrolytics is, the ESR varies wildly with temp and age. They can be fine, but used carelessly, they can make a poor choice that much worse. (In that case, the wiser choice would've been a stable-ESR type like tantalum or polymer, or a low-ESR ceramic or polymer with added external resistance.)
It's all a matter of "how much?" Some circuits are fine with a small electrolytic, or just one or a few 0.1's; others need a lot of both.
The determining factor is, how much voltage ripple can your circuit tolerate, and how much AC current does it draw? (It's not DC current that matters, it's the change. Say your circuit is switching rapidly between 0 and (lots)A, it's basically worst-case 100% AC*.
Anything else, probably easier.)
*Well, 50%, or something near there, depending on how you define it.
Tim