And it cuts both ways, if the Eagle gets enough speed to fill that role, then the Falcon gets stepped on.
Such is the nature of the two ships' current design. They're very similar in weapons loadout, ship system, and even esthetics. You have to admit, they're basically designed to be compared. The problem being weapons loadout effectiveness in Starsector is very much tied to the base hull. Some weapons just work better on some ships than others. If you don't want them to fill the same role (and I don't think there's a problem necessarily with that), then I think you need to break the symmetry between the two ships much more.
I too would prefer the Eagle to be worth the line cruiser designation as opposed to being a cheap DP blocker. The 17 DP with the ship 700 flux dissipation seems to work at first glance in a fleet context though, so if that is what we get I won't complain from a balance point of view. A preferred play experience point of view perhaps, but that is a lot more subjective admittedly.
To expand on what people are saying, given the job description, which includes holding an area but without finishing power (hence the low missile count and poor pursuit capability), about the only direction you can go would be damage absorption/survivability. I'll note Low tech uses it guns to improve survivability by having long range and fluxing up enemies before they can get too close. Eagle can't quite do that with only 3 medium ballistics, and beams essentially have no effect at long range since the enemy isn't firing, so 100% of dissipation can be used to bleed of the soft flux. So if you're not upping the firepower with mount changes or some kind of weapon specific hullmod, that means leaning into passive survivability stats and ship system.
So here's some brainstorming towards that end, namely having it be worth a line cruiser's DP as opposed to a light cruiser's without upping finishing power. These are not all intended at the same time, but just ideas that could be changed to make the ship worth more DP and also highlight the use of the ship as a tanky blocker to new players.
1) If the ship isn't intended to be fast compared to other cruisers, remove Maneuvering Jets. I think it is sending the wrong message to players and is almost like a tax which is limiting the potential design space. And Maneuvering jets invites comparison to the Falcon. Essentially it isn't a "choose this moment to use it" ability on the Eagle, but more of I need to keep hitting F every 10 seconds to keep up with the other ships. Which feels like busy work as opposed to engaging gameplay. Think of it as a quality of life feature that you don't need to constantly remember to keep pressing F. Bump the base speed and maneuverability up to compensate. Say to base 70 or 75 speed, and maybe 50% more turn rate?
2) Consider defensive ship systems such as Fortress shield or Damper Field. Or a brand new ship system. If you want to keep the "press every 10 seconds" nature, maybe something that has 50% up time and gives 50% more shield efficiency while up, but doesn't affect outgoing weapons fire in any way (unlike Fortress shield or Damper field). A shield AAF if you will. Or perhaps more engaging, a short duration charged system which when activated blocks 100% shield damage for 2 seconds or the like (again without preventing return fire) with a fairly long recharge time for the charges. So like a shield plasma burn - instead of dodging that bomber wave, you just tank the missiles. Gives a reason to have Eagles go first, to tanking the initial enemy fleet alpha strike.
3) Just straight up improve the shield efficiency down to 0.6 (so 33% more shield tanking) and extend the shields to 300 degrees or even 360, or alternately switch to a 180 degree omni-shield. Effectively give it a high tech flux/shield package. Or go crazy all the way down to 0.5 efficiency. Make the ship stats make it obvious it is a really tanky shield based ship.
4) Make it more obvious it's intended for fleet situations. Build in Nav Relay and ECM Package, which indirectly buff survivability (shorter range for the enemy means more time to drive flux up before they start firing) as well helping to protect the other ships. All that extra tonnage that is slowing it down is used as a command suite to coordinate better. 5 Eagles providing 20% speed and 15% ECM might have interesting large fleet implications that make up for the mediocre individual performance, although probably drops off heavily against Ordos. Perhaps a unique built in hullmod that improves fleet performance in another way?
Of course, I'm not the developer and the more extreme the departure from the current version, the more work involved, both in coding, graphics, and balancing.