http://electronics.stackexchange.com/questions/199479/ceramic-mlcc-versus-tantalum-capacitors

here are lots application notes on this. Google for Tantalum vs ceramic capacitors

Ceramic capacitors are best for it's ESR & ESL. So, that they can handle huge ripple currents at less temperature rise in power supplies. Same way don't disturb signal quality in High speed systems (AC coupling capacitors). But their DC Bias characteristics are poor. Like a 47uF X5R 6.3V is ~ 23uF @ 3.3V. This Low ESR & ESL may be bad at some cases. Like some Buck converters require enough ripple at the output to be stable. and lower ESL will react with cable capacitances to give unnecessary oscillations.

Tantalum capacitors best known for Volumetric efficiency and Cheap cost, but they have more failure cases due to surge currents. they have alternatives with polymer capacitors like POSCAPs.