I did some test too, comparing Sleep Dart and Biotic Rifle Shot. Here is the video:
I believe it could be more illustrative, since I've used moving target you can see that you must fire sleep dart much more far away from the target if you want to hit it.
I used practice range, being at second floor and firing at the most far away moving bot.
Sleep Dart:
46 frames from the moment of animation start (yellow ability icon)
to hit (red half circle at the bot)
28 frames from the moment of firing (bullet out of the gun) to hit
Rifle Shot:
14 frames from the moment of animation start = firing to hit
If shot speed is 85.5 m/s
Then sleep dart speed ≈ 85.5*14/28 = 42.8 m/s ± 9 m/s (taking into account 1-2 frame error)
If we taking into account sleep shot animation (46-28=18 frames)
and human reaction time (0.25s =15 frames), then we need to react ≈1.5 times earlier
with sleep dart than with rifle shot (at the given distance used for testing).