Why do animals use glycogen for their polysaccharide storage whereas plants use starch?
well glycogen can be broken down into sugars a lot faster, many more branches means many more ends to clip individual sugars off of, that's how you mobilize the sugar for use, it is clipped of the end of a strand. With many more branches glycogen can mobilize more sugar more quickly.  This is not important in plants but in animals that need to be able mobilize lots of energy in a hurry, glycogen works better. Additionally glycogen is a smaller molecule and easier to make, not surprising since glycogen is the ancestral condition for plants and animals. 

As for why plants switched to starch, or more precisely gained it through symbiosis, starches folded crystalline structure makes it a higher density energy store but also slows its release, it is however more stable, which is important if you are going to be storing it for a long time. Animals would likely switch to starch too if they did not have to break it down to digest it, just because they take in so much of it. But since they have to break it down there is no real incentive the build it back into starch when glycogen has some advantages and quite frankly since the pathway is already there and evolution has a lot of "eh good enough".