Generally, it's best to break the characters up into two groups: Batman/Nightwing and Robin/Batgirl. For speedrunning purposes, the former group edges out the latter due to their ability to hit multiple enemies much more reliably with charge attacks.

It's a shame, because Robin/Batgirl can run circles around Batman/Nightwing in terms of how many points they can earn/how quickly they can buy out and even outpace the store unlocks with surplus points. That being said, they get these points from dealing less damage, which means more knockdowns and subsequently more time lost. To be fair, they can get close times to Batman/Nightwing, but currently I simply cannot make them go any faster.

The final nail in the coffin was when I discovered that Tornado Kick, the final charge move unlock for Robin/Batgirl, does LESS damage than Elbow Fury, leaving these characters hurting for maximum damage off of a Power Combo. Meanwhile, Chainsaw Kick, the Batman/Nightwing equivalent, is absolutely devastating for damage and can even hit multiple enemies reliably.

With this preface out of the way, it is important to consider the minute differences between the two characters in each weight class. There are only character-unique animations for the basic knockdown moves (punch x3 / kick x 3), grabs, throws, and buddy moves, the latter 3 having very little application in a speedrun (although if it turns out that buddy moves are viable, that will be ALL of the hype).

Batman vs. Nightwing

Nightwing is the clear winner here. Since Batman/Nightwing's grabs are too slow and weak for speedrunning purposes, his one weakness, his much slower throws, are completely moot. Both of his knockdown attacks are significantly faster than Batman's.

Nightwing also has shorter speeches on average at the beginning of levels; Batman looooves to talk.

Robin vs. Batgirl

If you're brave enough to try and use one of these two in a speedrun, Robin edges out Batgirl, if only just. Their knockdown moves are near-indistinguishable in terms of speed, so it comes down to one thing: Throws. Batgirl's throw is extremely laggy, and its usefulness in a speedrun is marginalized by the fact that it much more consistently knocks down other enemies in a radius, costing you time.

Overall, while it currently seems clear-cut that Robin and Batgirl might need their own category, I remain optimistic that there might be some exploit down the road that could help them take advantage of their much faster attacks and higher point averages.