The second video does appear to be smoother in operation, but. You need to tighten those belts up. If your X and Y axis are not running perpendicular to each other and/or not parallel to the side rails. This should only effect the job, not cause the jittering that is being transmitted down the belts.
Have you tested the driver output voltage for both the X and the Y. I’m thinking that either one is running under powered. Try upping the voltage slightly to see if that makes any difference. But keep feeling the drivers heat sink, to ensure that they do not get to hot, while testing.