The only common these three different capacitors have is that they provide capacitance. But they provide this by totally different topologies!
The main difference for the user is, that they deliver drastically different equivalent series resistance. This influences the amount of suppression of noise: The smaller the equivalent series resistance the more effectively they can suppress noise. From this point of view the 100nF multilayer capacitor is better than 100nF tantal, which is better than 100nF aluminium electrolytic.

In some cases the EMC specialist can use the characteristic equivalent series resistance of these capacitors to find an optimal filtering solution, though.

Another issue is reliability. Here the aluminium electrolytic shows the poorest performance, although drastical improvements were made in the last years. An aluminium electrolytic often quits its service life with an increase of impedance, the capacitors tends to 'dissapear' more and more. The tantal likes it to quit its service life by introducing a short circuit! Not a nice way, as without current limiting an explosion can occur.
With these both types of electrolytics reliability is not only a theoretical issue, they do really die from time to time! Just two weeks ago I had a tantal short circuiting in an rather unspectacular circuit, a sine generator. Means no heavy ripple currents or other service life shortening signals were applied to this cap.

Ceramic multilayer caps are a milestone in the improvement of reliability of decoupling caps. Without their inventioning DC/DC-switchers wouldn't work that reliable as they do.
Happily, multilayer caps are manufactured today in the range of even tens of microfarad, and this even in 0805 packages,or smaller! These caps offer the best noise suppression performance ever.

Kai