Polymer type capacitors have several advantages over a normal Aluminum Electrolytic Capacitor. The polymer electrolyte has higher conductivity than the liquid electrolyte used in standard capacitors, resulting in lower ESR. This permits a single polymer type capacitor to replace several aluminum electrolytic type capacitors, resulting in reduced board space and total number of components on the board. Since the polymer is a solid, it also gives longer life, not following the classic Arrhenius formula. Instead of doubling life with every 10°C drop in temperature, the lifetime will be 10 times longer for every 20°C decrease in temperature.
Yes, they are a little more expensive, but for circuits where having low ESR is importnat ( Power Supplies ), they can make a big difference!