Speeding up by a given amount and slowing down by the same amount takes exactly the same amount of energy! Also, it doesn't matter where you stop if you're trying to avoid the errant driver who blew a red light, what matters is that the change you make prevents you from trying to occupy the same piece of space at the same time as him. Also if you brake then if the collision does occur, there is significantly less energy to dissipate afterwards than if you try to accelerate and the collision occurs.
You *want* the ABS to kick in. Unless you're super driver then ABS will stop you quicker, it's what it's there for. Even a reasonably high performance car will decelerate twice as quickly as it can accelerate.
A summary of some calculations given in a reply to someone else, in the case of both cars approaching at 40mph (18 m/s) with a best case time decision for when you can say the other vehicle is going to just blow on through the red light: with the best case acceleration in a reasonably high performance car (say, a Focus ST with a sub 7 second 0-60 time) will mean you miss the collision by about 1 meter. Mashing the brakes and letting the ABS do the work will mean you miss the collision by around 16 meters. Even in the pouring rain and halving braking performance, if you brake you'll avoid the collision by nearly 10m. In a normal car, for instance a normal Honda Civic, accelerating will not avoid the collision but instead worsen it as you now have more energy to dissipate after the offending red light runner clips the rear corner of the car. Accelerating to avoid colliding with a red light jumper only makes sense if you're in a Bugatti Veyron or a Lambo or a Ferrari, or a performance motorcycle. But even so braking will be safer since these vehicles have very good brakes and tires.