With this specific LAX approach FLCH seems the preferred option. I say that only because VNAV normally requires a spot of speedbrake to keep you on the path and speed, whereas FLCH doesn't normally need it. I've done it quite happily in VNAV with a reasonably strong headwind and it's managed without speedbrake but most of the time the winds are not strong enough to enable that. Of course, not using speedbrake is purely a pax comfort thing and if I needed it I'd use it but that doesn't seem to be the case in FLCH on this arrival, so why not keep it less rumbly down the back? If you notice on the video at around 1:40 he's at the correct speed but about 1100' high on the VNAV path. To correct that and stay at his assigned speed he'd need a bit of drag but in FLCH he has a nice, constant descent, abides by the altitude and speed restrictions and all without using the speedbrakes. All very nicely done, I reckon, and probably shows that whereas VNAV is perfectly okay to use, FLCH worked better on this particular day.