I've tried (and own) both. I do not have a tremendous amount of experience with either, and I'm about to switch to an Ingenuity rail on my stock, rather than the RRS VYCE I've been using (so that may change things). That said - the biggest issue I had w/ the ball head (an RRS BH-55) is that there's a lot of room for the gun to flop. Even with the drag set high enough to provide good resistance, it can be hard to keep the rifle upright. The ball wants to tip over, for me. If I set the drag high enough to avoid that, it's basically locked in place and difficult to transition the gun.
The leveling base seems more stable, and is easier to adjust to move controllably for me. The downside is the reduced range of motion (which prevents the "flop", but means I may have to manipulate the legs mid-stage, depending on the stage).