Side dump is handy when a long narrow pile is preferred, instead of a "traditional" dumps fat round pile.
With a side dump you can dump your entire load quickly, without needing as much height clearance.. for example, inside a building with 12 foot ceilings.
Alot of grain beds have little "doors" that slide up and down on the side, so you can regulate the rate of dump.
For instance, lets say you have a load of grain you wanna feed your cattle.. by opening the side "doors" up a little bit, tilting the bed and driving forward slowly, you can leave a nice long pile of grain or corn for your cattle to walk up and eat.
Another practical application.. lets say I have a load of stuff I wanna dump in a roll off container (like a roll off dumpster) you just pull up along side, drop the side of the bed, and dump. The load gets evenly distributed in the container, and no hassles backing up, and no giant mound in the center sticking up.