Just for curiosity. I don't find enough information about this, even in documentation. I don't see any difference when I use it.
It controls whether to keep intersecting edges perpendicular to the bevel direction.
Loopslide On: gives smoother topology and better results for tight geometry
Loopslide Off: keeps perpendicular edges and even bevel width
When Clamp Overlap isn't enough, Loopslide On can keep the topology in check:
I am the bevel tool and modifier author. Loop slide does the same in both. It only has an effect if there are unbeveled edges between two beveled edges at a vertex, and furthermore, at least one of those unbeveled edges is in a different plane than the one containing the two beveled edges.
In a circumstance like that, there is a choice where the meeting point of the offset edges from the beveled edges go. (1) it can go at the place that best makes the bevel width match the amount specification; (2) it can go on a non-beveled edge between the two. The second may be preferred if you don't want the silhouette of the object to drastically change. That second method is what is turned on with "Loop slide".