Skis and Snowboards have 3 basic constructions; Sidewall, Cap, and a Hybrid of the two. Sidewall is a more costly way to build a ski. Years ago skiers would only see the highest end of skis with sidewall construction. The rest of the skis were "capped" with a sheet of fiberglass, and foam was injected into the ski. In recent years a hybrid of the two constructions became available. K2 was the first to do this in their snowboards, sidewall almost the entire length of the board that would taper into a cap at the contact points on each end. Maybe I've lost you at this point with all this Sidewall-Cap-Mumbo-Construction. The image on the left is what a standard sidewall construction looks like, and on the right is your standard cap construction.
If you take a look at the image on the left, the sidewall construction, you'll notice the pink abs sidewall, the cap ski on the right doesn't have it. ABS is a dense heavy material that is used to make skis stiffer torsionally, have better edge grip, and more durability from impact. If you want skis that will be more stable at speeds, have a little more pop/acceleration out of the turns, and be able to take harder impacts on rails and boxes, sidewall is the way to go. The downside with sidewall skis for park shredders, is the sidewall constructed skis can be more susceptible to damage, from skis crossing and edges digging into the sidewall. The material used to create a sidewall is also heavy, cap skis don't have this heavier material.
Because cap skis don't have this heavier material going the length of the ski, they are much lighter, especially in swing weight. So if you're looking for a ski that is going to be easier to spin or feel more nimble, cap is your answer. Cap skis top-sheets are also less susceptible to damage because of the rounded off cap going from top sheet to the edge of the ski (See Cap Image). The downside with a cap construction is less torsional rigidity meaning they are less stable at higher speeds, and less pop/acceleration coming out of the turns. Both types of constructions have their pros and cons, that's why manufacturers have started building a hybrid of the two constructions.
K2 Snowboarding was the first to come up with idea of combining the two constructions, and in my opinion they did the best job of it, they also patented it so it's only in K2 products. K2 calls it Hybritech, sidewall construction almost the entire length of the ski or board, then it tapers to a cap for a lighter swing weight but still all the benefits of a sidewall construction.
Armada and Atomic also build a hybrid of the two constructions, except in their skis, it is just sidewall underfoot for better edge bite, durability from impact on rails and boxes. The entire shovel and tail of the skis are capped for a low swing weight and durability of the top-sheet.
All of the constructions have their pros and cons, it's up to you to decide which type of constructions make the most sense for your skiing or riding. If your Mom is going to kick your ass for ruining the top sheet of the new park ski she just bought you that was supposed to last 3 years, go cap.