I see a couple of features that could improve the usability of Audiosnap (like being able to reset stretching of individual markers by a button/hotspot next to the marker instead of by the context menu), but mostly just a different workflow.
One thing I see that might really be a significant conceptual difference is that disabling stretching on a marker does not completely undo all stretching but leaves it stretched proportionally in the context of the markers to either side of it. SONAR doesn't do that; each marker has a stretched position and an original position, and disabling stretching on individual markers is going to return them to their original position without reference to how the markers on either side have moved. In SONAR, you would have to undo all stretching, disable the marker on the transient you don't want snapped, and then re-quantize.
You have to keep in mind that the videos like this always present an idealized situation that shows off the program/feature to best effect. I don't see that SONAR would have any trouble achieving the same result with the same material