In power capacitors, there are two types: APP (All Poly propylene) and MPP (Metallized Poly propelene). Which one is better and why?

Both are better, non is worst.

Depends upon the situation what suits you better. APP has more losses and long life, operation is costlier than the MPP. MPP has lower losses and lesser life. Operation of MPP is cheaper due to reduced losses because of the Construction Differences.

It depends what fit to your priorities. If you prefer continuity of operation of the equipment over the operation cost, you'll go for APP and if you prefer the lower operation cost, and ignore the shutdown time and maintenance of the equipment that might need over the time, you'll go for the MPP.

Its all your choice as per your needs.

There is another type of capacitor which is called Mix Dielectric Capacitor that uses two dielectric mediums. Its durability and losses and life span falls in between the above two. Life Span is more near to APP, losses are more  near to MPP. And this can be a better choice in many circumstances.