I tend to agree with the OP, the design is fighting against itself.
I'll go step farther and make the claim the Eagle doesn't actually have a ship system. It has a ship disadvantage which is active 50% or more of the time (the time when manuevering jets is off). Falcon has been bumped to speed 80 at this point, and has the same weapon combination as the Eagle, albeit with all the other stats and mounts at roughly 2/3 the count.
And speaking of pure pedantry, Eagle should cost 21 DP because it's 133% of a Falcon which is 14 DP 
I'd argue Eagle should only cost 21 DP (150% of a Falcon) if it has the roughly the same speed as a Falcon. Otherwise, there's a huge effectiveness malus on those guns and shields due to inability to position them where you need them as well as you can on a Falcon.
The fundamental game or ship design question I have is why doesn't the Aurora have a speed of 55 or 60 compared to the Fury's 90, in the same proportion as Eagle to Falcon? It is also roughly 50% bigger in terms of weapon mounts, just like the Eagle to the Falcon. What about the Eagle means a Falcon should be speed 80, 105 on average, while the Eagle sits at 50, 75 on average? Clearly if the weapon package is designed for that speed (i.e. Aurora/Fury) its OK to have a cruiser go that fast. If the Falcon isn't considered overly strong at speed 80 right now with it's medium ballistic + medium energy mount setup, can someone explain why the Eagle would be overly strong at speed 70 or even 75?
Can some one point out an advantage to me that the Eagle has over the Falcon in a campaign/fleet combat setting that demands such a huge speed disparity? Is it the 250 extra armor? But you have to go through Falcon armor 3 times compared to going through Eagle armor twice assuming same DP expenditures.
For example, do 3 Falcons really get in each other's way that much more than 2 Eagles? Isn't the fact that you have 3 ships in general better, with total base flux capacity (3*7000 =21,000 compared to 2*11,000 = 22,000) and base flux dissipation (3*400=1200 vs 2*600=1200) being virtually the same? Even OP wise, you're looking at 375 versus 310, with 50% more cost for hullmods in some sense. If you spend less than 65 OP on hull mods on each Falcon and Eagle, then the Falcons even come out ahead in OP. I was under the impression, PVP tournaments typically show that more cheaper ships are favored over fewer more expensive (in DP) ships, since it allows more of them to fall back and vent while pressure is consistently put on.
It just seems like the logic goes, it's bigger, so thus it must be slower. Which from a game balance point of view due to venting and shield flux mechanics, doesn't seem to quite hold up if everything else is in the same proportion.
Converted hangar Xyphos. Even of Eagle it's better than using ship-mounted Ion Beams, they have atrocious stats.
Alex on his way to nerf Xyphos again because people refuse to use the god awful Ion beams 
I know you're being a bit silly, but I'd argue Ion Beams are OK to good actually. Base range 1000 ion damage which wants to be used on armor/hull, and has shield piercing at high hard flux. It typically has more impact than a Gravition beam on a fight, and so a higher flux cost I think is warranted. Xyphos just happen to be even better (shoots over allies, PD that doesn't go down when overloaded, no flux cost, can be mounted on any ship of destroyer size and bigger, despite mount types). Doesn't help that Xyphos are the only real range 0 support fighter (Mining pods are just regenerating armor).
It really is the medium energy slots that are the problem here. Everything else about this ship makes it the most generalist cruiser to ever exist, which is a perfectly valid role. The medium energy slots just let it down. If you look at every single one of the medium energies, the problem is as clear as day.
Which brings us to the elephant in the room: How do you make a medium sized weapon generally strong without making a hi-tech hull overpowered in the process?
Don't forget the 5 small energy mounts as well on the Eagle. If those were kinetics, we wouldn't be having this discussion, since it'd be a Pirate Eradicator with energy mediums instead of 3 small missiles.
Essentially, the only option I see if you buff beams. Currently, high tech beam ships are considered sub-par anyways, so if you buff beams up, that potentially opens up more support styles for high tech ships instead of dash in/dash out burst DPS builds. We've just had a thread about Furies (and Auroras) complaining all the sensible builds use heavy blasters and sabots. Not a single Graviton beam or tactical laser to be seen in those loadouts.
I think Alex was trying to do something along those lines with the high scatter amplifier, make beams better, but that was just moving the beam weapons into the weapon space already occupied by Heavy Blasters, Pulse Lasers, and IR pulse lasers. Make them good enough and you ditch the blaster/pulse weapons. Make them too weak and you ask what's the point? And with a hull mod, its not like you can tweak the effect for each individual beam type weapon (let alone mods).
Essentially, you need to double down on beams being reasonable support weapons. One way you can do that is add additional perks, as opposed to raw damage, to beam weapons either inherently or via hullmod (like Advanced Optics). You'd think weapons with ranges of 1000+ITU+200 would be good, yet I don't see long range beam spam fleets being espoused as the greatest thing ever.
I did like the idea of changing high scatter amplifier to another support beam hullmod instead of a hullmod which turns support beams into weapons which already kind of exist. Amusingly, Eagle can fit more beams, with more overlap, than a Fury can, at the soon to be same DP cost. A hullmod that made beams pass through allies (like the Paladin system) would turn Eagles (and Falcons) into the premier anti-fighter/long range anti-missile ships and give them an interesting cruiser escort role (along with Furies and Auroras). Probably would also want to throw on +10% beam damage or something given it doesn't actually help a solo ship, or even a small fleet.
Right now, I consider carriers, missile ships, and destroyers with converted hangar Xyphos to be the best escorts, since they can actually assist the fight in front of their escort while sitting behind it. Also, a destroyer pack with Xyphos has excellent support coverage against fighters and missiles.
