I've had original/xl/new xl. The original first 3DS (at least mine) had a SHIT AWFUL loose d-pad (really really really bad.) FLOATY-ass button, stuck to your thumb, I would consider it a disgrace from Nintendo. I can't believe they still manufacturer that trash.
The New 3DS XL (at least mine) there is a little "play" in the d-pad, but I would consider it very similar and on par with dsi xl d-pad. I can't really tell in your video if it greatly differs from what mine looks like, but there is always a chance you have a different build (I can cite numerous unfortunate inconsistencies with Nintendo devices.)
DSi XL had a clicky/mushy d-pad, it has a steeper "apex" than the GBA SP, so you need to put more movement in "rocking" the pad around. The GBA SP model has very "shallow" buttons rather than "mushy" style like SNES/GC/original GBA. So the GBA SP is much more sensitive that way, it boils down to personal preference
original XL (at least mine) had a much improved d-pad, but still way more floaty than I would like. The New XL greatly improves this, and personally I'm fine with the New XL d-pad entirely.
To keep going with the comparisons to classic d-pads, I compared the feel of the original NES d-pad, and the difference in play is the NES d-pad tends to "slide" (like the motion of the circle pad) instead of "rock" around and float, memories of a great controller but painful thumbs.
the GC d-pad is really tight, I wonder what the NES and GC pads would still be as responsive if the corners/edges were smoothed down for comfort; would there be a major tactical and tactile sacrifice?