Well, the drones from the challenge are meant to fly faster if you get closer. You're just chasing it to the end point.
Can't help ya with birds. I do cut corners and catch them pretty easily. I'm pretty good with swinging too. The boosted point jump is really powerful.
The problem is that the birds speed up if you get too close. I got within 10m of one last night and watched it zip forward to about 50m away. It's like there's a point in their flight path that they have to reach before you can web them.
I've noticed it with car chases as well, but not all of them. Some of them you can press triangle as soon as you're within range, but others will get sudden bursts of speed to get away from you if you get too close, too early. The
Helicopter chase