Neither can I to be honest, as most of my predictions end up being wrong. Having said that there are few possibilities.
First I should probably mention that while I couldn't be bothered to write it up, I actually did finish this initial missile exchange (after two whole days of non-stop computing with seventh gen i7). There was no damage to the Kinharans but the missiles got all the way to the energy weapon range. That however does not mean that much. As the Confederation knew more missile waves will be coming they were not firing at their maximum possible speed, instead trying to limit ammunition expenditure. Once that was done the Hegemony bombers would die, as the enemy interceptors were equipped with a single 100m railgun. That would also make them respectable point defence weapons.
Once that was done the next step of the battle would be short range missile exchange. The Kinharans know they cannot hope to penetrate human defences well enough from long range, so even though they have superior missile ranges they would not fire. More importantly, they cannot know whether or not they have equivalent energy weapon reach and if they don't, missiles would be their only hope of surviving, making it even more important for them to fire for maximum effect - which means minimum range.
This would open some options for the Hegemony, but there wouldn't be much they could do with that. Obviously they could fire from long range, retreat and repeat, grinding the enemy down with multiple strikes. Unfortunately there are two problems with that. First the attack through a jump point succeeds because the defending side cannot hope to picket it at full strength at all times, due to maintenance and morale issues. But they can do so for a limited time, so if the human fleet withdraw from the system, they could not hope to return any time soon without fighting a full scale battle at the jump point, which would be equivalent to short range exchange but worse for humans, as their forces would be dispersed and suffering transit effects for a short time. So since a short range battle would happen anyway, doing so in deep space, as a concentrated force would be preferable.
Second the Hegemony simply doesn't have enough missiles. They had large enough industry to support new construction but until now they never fought a proper long war and they were simply unprepared for how much ammunition it demanded. They are expanding their industry and by now they have over five thousand ordnance factories, but their stockpiles are rather low and it will take time for them to build them up. Plus truth be told five thousand factories isn't that much.
So as a result I intended the Hegemony force to close to one million kilometres and fire, with the Confederation firing as well in response. One important thing to remember - the fire controls in Aurora are very basic, which means the anti-missiles would be fired at the nearest threat and interceptors are faster. So it is very likely that most anti-missiles fired in this situation would be fired against enemy anti-missiles, making them next to useless, especially if both sides fire anti-missiles just before firing their shipkilelrs as decoys. I could assign targets by hand.... but that just wouldn't happen, not with several hundred ships, even if Aurora was properly responsive. As an additional note, the Kinharans suspect the larger ships are carriers, so they wouldn't be targeted, as their bombers are destroyed. I'm not even sure I would brought them into range anyway, but by the same token their very large size, and CIWS make them very resilient to fire, making them reasonable missile soaks, so I probably would bring them in.
And this is where my ability to predict things is at an end, as I simply can't even hope to guess the results of this exchange. As eleven largest Hegemony warships are either carriers or jump battleships, and they have all those other jump ships with no armament, they have effectively only about six million tonnes of shipping against thirteen million tonnes of Kinharan shipping, but they also have superior technology, they have many assault destroyers which have heavy missile armament and their jump battleships have not only very heavy gauss cannon armament, but also anti-missiles in single shot box launchers, theoretically ideal for this kind of combat. In addition while both sides have the same energy weapon range, those ranges are greater than they were at the start of the war and the Kinharans were unable to upgrade their ships. As such the Hegemony may actually have an edge in beam ranges.
Of course the Kinharans had a surprise for humans - microwave beams, which would disable sensors and fire controls. But I'm not sure what kind of impact they would have.
In the end, unless the Hegemony have achieved crushing victory (which seems unlikely) the war would have moved to another stalemate.
If the Kinharans won, they would not even dream of attacking, as they simply do not have enough strategic depth to risk it, especially with their technological inferiority. If they were turning to be too tough a nut to crack for the Hegemony, I might have make the Confederation attack due to popular pressure, demanding liberation of those left in the Albuquerque system, but even if I did this it would not have happened for years to come.
If the Hegemony won, but sustained heavy loses, that would be that. The government would be unwilling to further uncover their core systems, so any reinforcements would have to be a a new construction, and more fighters would be needed. I should also probably point out that a couple of carrier groups were formed without any larger escorts (frigates only) to support the war and at least one other group was further stripped of destroyers and cruisers to support the newest offensive. As a result, while the capital is protected by several carriers with full fighter groups and large number of frigates, the number of larger escorts is very, very limited.
In addition the Confederation was planning on establishing proper jump point defences, consisting of barely mobile bases (just a single engine for redeployment) with very long endurance. So far those haven't been deployed because there aren't enough of them to survive the kind of attack the Hegemony could launch, but they could halt further human offensive if the loses of this battle were heavy enough. In addition, while I haven't specifically checked that, there should be more ships in training and I know there are many picket ships (deployed because of Auroran degradation of stability without enough forces) that could be called forward. Even if that wasn't the case, if the Hegemony was victorious, but left with only a couple of dozen ships and empty carriers, they simply could not risk attacking anyway. Which is why unless the battle ended up being very one sided and in favour of the humans, a new, possibly even longer stalemate would happen.
