The 3 HAC Eagle provides more shield pressure than the champion (due to accuracy) for longer and for less DP.
That is just not true...
I just typed out all the numbers, I'm not going to again. 2x HAC (or needlers) + plasma cannon + squall (a realistic champion build) does the same shield DPS as 3x HAC + 3x pulse laser (a completely overfluxed eagle build designed to max shield DPS). The non missile DPS (2x HAC + plasma) is 300+ more shield DPS than 3x HAC. So if you run beams in medium slots on eagle, you are way behind on hard flux shield DPS. 2x gravitons + ion beam is like just keeping up on total shield DPS (ignoring squalls and ignoring that some of the eagle damage is soft flux lol).
You could also run autopulse and IR pulse lasers (or even a volatile particle driver) to further max out shield DPS on champion. But I think plasma being amazing hull/armor DPS is much more valuable. The fact that the champion build can kill stuff easily and that eagle has terrible hull/armor DPS while just keeping up on shield DPS, is also kind of telling.
You're not going to type out the numbers because you're wrong. You cannot be like "the 3 pulse laser eagle is massively overfluxed" without acknowledging that the Plasma Cannon uses up 825 flux per second on a ship that has less base flux than the Eagle or that you don't actually want to fit 3 pulse lasers on an Eagle.
The Champion, with a flux distributor, has 940 flux. If it has 2 HAC and a Plasma Cannon its got 428 Flux from the HAC and 825 flux from the Plasma Cannon. This nets a long term total weighted shield DPS of
1204. Plus 512 for the squall while it lasts. Makes 1716. This assumes its shield is not raised. You get a bit more out of HEF but not enough to quibble about an extra 7.5% DPS from the Plasma Cannon. Up to 1247 consistent DPS and 1761 when the squalls last.
The Eagle, with a flux distributor has 990 flux. If it has 3 HAC making 642 flux and an Ion Beam making 200 Flux its using 842 flux out of 990 and putting out 1334 long term shield DPS. If it has a single graviton its making 1534 and its STILL under flux budget. If it has two gravitons its only 3 over flux budget and making 1730 shield damage per second. With better accuracy(hardpoint recoil!) and longer range(well except for the squalls). Not subject to point defense. And without worrying about ammo.
If you want to count shield usage (or remove the flux distributor) then the eagle is even better in consistent DPS even though its shield is slightly more expensive. Because far more of its weighted DPS is going into its HAC than energy damage and none of its DPS disappears when the missiles do. Plus you can drop the Gravitons if you really want. With the Gravitons its better in terms of raw numbers but without them its better in terms of overall survivability(you can use the OP for point defense saving your damage on your shield... which is also damage to your DPS). 1188 shield DPS here[1306 with gravitons fit]. But the Champion is only making 955 consistent (though in this case its making more[1400 ish] until the squalls run out)
If you want to count sustainability then the Eagle is better here too because the eagle has 10% more base shield capacity and its 15 speed faster. Armor and Hull are not the only way in which ships tank especially when on the line.
"but what if i efficiently shoot the Plasma Cannon!" But you won't. And the AI
certainly wont.
So while the Champion is probably an altogether stronger ship is simply does not dominate the eagle. The eagle has things for which its good at, its just like marginally over priced. It is actually 15 speed faster than the champion once you account for its ship system. It actually puts out more consistent shield pressure than a champion.
Like. An AI Champion fit as you describe cannot kill an AI Eagle in the sim before it runs out of squalls when the AI eagle is fit with only Heavy Mortars in the front and gravitons in the back which is an absurdly bad fit and i think that the only reason it will kill it before time runs out is because the Eagle is likely to get wedged on the side.
That doesn't mean that that champion is bad. But it really isn't just better than the Eagle at all things.