The Main Advantage: Smoothing the Fork Tube Kink
Have you ever seen a rider flat land a jump or some similar hard hit, in slow motion or as a still image? You may be surprised at how much the forks flex! And they're actually always flexing, it's not just from very hard hits, they flex all the time at various levels. The key point here in regards to the split clamps isn't that the forks flex, it's how and where they flex. The fork assembly is free to bend without support (aside from the structural properties of the fork itself) from the axle all the way up to the triple clamps. But the triple clamps are relatively stiff, and they are what mates the forks to the rest of the chassis. So, the relatively smooth bending of the forks turns into a kink at the bottom triple clamp.
You can see this kink exaggerated in the photo here. As the forks compress, the bushings that the inner fork tube slides on will pass through this kinked spot, which causes some binding of the suspension, and a harsh feeling for the rider. Anything that can be done to minimize the kink in the forks will allow for smoother suspension action and a plusher ride. And that's what split clamps do. The separate clamping areas are able to flex independently of one another and smooth out the kink. The kink is still there, there's nothing that can eliminate it in a traditional suspension fork design, but it's slightly reduced by using split clamps.
We can show the details of the kink with some finite element analysis. Here's an FEA result representing a hard landing that's causing the forks to bend. We can look at how the fork tube kinks with both our Gen1 (solid/traditional) triple clamps shown on the bottom of the image and our Gen2 (split) triple clamps shown on the top. These happen to be KTM/Husky clamps, but all fitments will be similar. We can plot the fork tube deflection vs. distance along the fork tube to see how the tube kinks (more specifically, we're looking at deflection of the inner diameter of the fork tube). The traditional style clamps are shown with a solid red line and the split clamps are shown with a solid blue line on the graph. But from this plot, it's not so obvious what's going on. To more easily see what's happening, we can take the derivative of these curves and see the slope of the fork tube bending along its length (see calculus is useful!). The slope of the fork tube is shown by the dotted lines. Ideally, we'd have a constant slope that doesn't fluctuate much as that represents a kink in the tube that binds up the suspension. You can see the slope of the split clamps is a little smoother (dotted blue line), especially right where the triple clamp starts to clamp on to the fork tube.
So how much of a difference does this make in reality? Well, it's not a night and day difference by any means, but it is noticeable on the track. Clearly a traditional clamp isn't terrible as we've all been using them for a long time, and many championships are won with them. But any small improvement is a step forward towards a more comfortable and faster ride. One important thing to note here is that the split clamp only helps this issue with the bottom clamp. The top clamp being split doesn't help with this at all as the fork bushing never slides through the top clamp clamping area.