A few points:
The amount of fuel you carry is kind of insane... 194,052,000 litres versus 750,000.
This is actually a good point, but not in the way it is posited. ~200m litres of fuel comes out to about 4,000 HS, or 20% of the total displacement, which is indeed excessive. Notably, the engines add up to "only" 6,280 HS which gives around a 5:3 ratio of engine to fuel mass - this is quite bad, as a 3:1 ratio is optimal and divergence should nearly always be in the direction of a higher engine mass to conserve fuel. That being said, for a 10,000 HS propulsion section it is still very reasonable to have somewhere in the range of 2,000 to 2,500 HS of fuel, or about 100m to 125m litres, although I would expect in practice to see somewhat less than this (but not a mere 750,000 litres!) as large warships usually need to use low-efficiency engines to conserve gallicite and fuel stockpiles.
Your Active sensors are also a bit worse than mine.
This is incorrect: the Andrew variant has a range of 204.5m km on its RES-200 active, whereas the Blogaugis variant has only a range of 113.8m km on a RES-50 active. The Andrew variant will easily spot the Blogaugis variant first by a considerable margin.
But, if we also include finding an enemy in this competition, You'd have a bit harder time - I'd have noticed Your ship coming earlier. And with my EM and Thermal signature, it may take a bit of a while for You to find mine. In the meantime I could track and sneakily try to evade You... Unless you drop your speed or something...
Almost certainly what will actually happen in practice is that the escort/AWACS/recon vessels escorting both ships will spot the enemy fleet. I want to point this out because it is important not to just compare two capital ships as if they would engage in a 1v1 duel for supremacy - this is a recipe for a dead capital ship.
So the first wave would be missiles.
This is where things are going to be one part interesting, three parts tremendously disappointing.
Let's get the trivialities out of the way first: the Blogaugis variant carried a grand total of 40 missiles, dealing two damage apiece, and can fire 10 at a time. This would be utterly trivial for the 122 10-cm railguns of the Andrew variant to swat away, but even if all the missiles hit they deliver a grand total of 80 damage. The Andrew variant can recharge its shields to completely erase this damage in ten seconds. Score zero for the Blogaugis variant.
The Andrew variant is far more interesting, as it packs 5,000 size-5 missiles. While the missile specs are not given I would assume, conservatively, that these missiles pack at least 4-damage warheads, so delivering about 20,000 damage i every missile hits. If we assume that all 5,000 box launchers fire at once, as one would expect when engaging a million-ton titan, how much damage will actually be done?
First of all, we're going to have to run some point defense calculations - I'm going to assume the Andrew missiles have a speed of 12,000 km/s, because this is entirely achievable with very low NPE-era tech (frankly I would have used 15,000, but I want a conservative estimate here). In the single final-fire point defense volley, the Blogaugis variant will fire 560 shots with 8000 km/s tracking speed thanks to turrets (66% accuracy modifier), and 72 particle beam shots with only 2000 km/s tracking speed (16% accuracy modifier), all using fire controls with 80,000 km maximum range. PD final fire takes place at 10,000 km, so the BFC speed gives an accuracy modifier of 87.5%. Summing this all up and applying the appropriate accuracy multipliers, the Blogaugis variant will shoot down on average about 340 missiles, leaving 4,660 to score hits (no chance of dodging with only 50 km/s speed).
Those 4,660 hits will do, based on our assumptions, around 18,600 damage. 100 of that is absorbed by the shields, leaving 18,500 damage to impact the armor directly. The Blogaugis variant has a total of 89,000 armor boxes on account of being really big. It is tricky to actually work out armor penetration probabilities without a direct simulation, but as a rough rule of thumb a heavily-armored ship will lose around one-third to one-half of its armor before beginning to suffer penetrating hits, a margin the Blogaugis variant comfortably exceeds.
So the result is that the Blogaugis variant is hilariously impotent, while the Andrew variant can deal a lot of damage, but will likely fail to even penetrate the armor of its opponent let alone destroy it. Overall the advantage goes to the Andrew variant but tactically this is a draw.
Your 12cm Railguns would be in range, while most of my weapons won't... Would my particle beams be able to do something? If tracking speed is the same as my ships's speed - yeah, they're useless. But if 2,000 - I might be able to retaliate...
If You decide to go closer and unleash all the Railguns you've got... Well, I also can retaliate with Lasers and Gauss cannons. Mesons, however, would not help.
At this point the Andrew variant runs away and reloads, because it has a top speed well in excess of the orbital velocity of Mercury. It does need to reload at a planet, which is a serious logistical handicap, but by the time it has done this and returned to the battlefield the Blogaugis variant has traveled about 10% of the way back to a repair yard to fix its armor.
Of course, in a real battle which is between two fleets and not only these two ships the Andrew variant likely has not wasted its time targeting the enemy capital ship, instead shredding the entire escorting fleet with 20,000 damage from missiles before running away, which would be a crushing defeat by any standard.
Edit: Also - good luck building a tanker (fleet), that can supply this thing...
To be frank, if you are building million-ton monstrosities without the logistics infrastructure to support such things, you have made a serious mistake. It may take multiple large tankers to top off such a large ship, but a 150,000 or 200,000-ton tanker can easily tote around over 50m litres of fuel, and that is really not a difficult size of commercial ship to build. The greater challenge is harvesting all of that fuel, but if you have expanded a shipyard to a million tons without building several hundred fuel harvesters in the interim period I do not know what else to tell you.
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To conclude, I want to return to an earlier point, and note that nearly all of these issues would be at least mitigated if not entirely resolved by putting an actual decent propulsion section on the Blogaugis variant which can allow it to at least be competitive in terms of speed and range against contemporary vessels. At only 50 km/s there is simply no way to bring the beam weapons to bear outside of a JP defense scenario (and even then a competent squadron jump likely mitigates this). If one is going to build a beam-primary warship, one
must bring enough speed to close the range, otherwise the beam weapons will be entirely ineffective outside of perhaps surprising the enemy in the initial encounter (mainly applies to NPRs).
