The soft-covered PlyoCare balls are primarily meant for submaximal throwing and for constraint training, as well as general arm care. They’re not meant for throwing as hard as possible with zero mechanical intent to change; the point of PlyoCare balls is to provide a larger tactile feel in the hand that removes the connection to a baseball, further distancing the athlete from the idea that he has a baseball in his hand. Additionally, the large variation in weight between the balls creates greater changes in movement in the constraint drills (Pivot Pickoffs, Reverse Throws, Walking Windups, etc) as well, while the weighted baseballs have a much smaller weight distribution.
Here’s a short video of a comparison of two big leaguers using PlyoCare balls to subtly alter arm acceleration pathing back in the 2013 and 2014 off-season:
On the other hand, Driveline Elite Weighted Baseballs are almost exclusively meant for maximal intent throwing to build velocity or to affect changes at near 100% intensity for other aspects, like command or ball spin axis alignment. The black 11 oz. ball is often used for warming up purposes when it’s colder outside or to get ready in the bullpen quicker, as the heavier weight will allow the arm to lay back in external rotation easier and provide a better dynamic stretch.
Here’s a good example of how the weighted baseballs are used for our weekly velocity-development featuring Casey Weathers (Indians):