Ceramic (MLCC) versus Tantalum capacitors
There are lots of application notes on this.
Google for "Tantalum vs ceramic capacitors".

Ceramic capacitors are best for its ESR &amp; ESL. So that they can handle huge ripple currents at less temperature rise in power supplies. Same way, they 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 &amp; ESL may be bad in some cases. For instance, some Buck converters that require enough ripple at the output to be stable. And lower ESL will react with cable capacitances to give unnecessary oscillations.

Tantalum capacitors are best known for Volumetric efficiency and Cheap cost, but they are prone to failure due to surge currents. There are alternatives like POSCAPs (polymer capacitors).