I was going to post about what I thought of the capstone skills when I got around to it, but guess I'll just post here instead

First, I like the current system in terms of its structure. I think this new tiered system works well, so I don't see any need for fundamental changes.
However, my understanding is that each capstone is meant to be approximately equal in power, i.e. the player should "want" to take each one about equally as much. But that's not the way it ends up. Going through the list:
Systems Expertise: Good for some ships, fairly useless to others, so it really depends on the particular ship. Giving +15% CR as an elite bonus would be interesting, except then it'd sort of make Combat Endurance superfluous, since Crew Training is in level 1 Leadership without any other prerequisites so it's almost always taken. Perhaps if Crew Training gave +10%, SE gave +10%, Combat Endurance gave +10%, and BotB (more on this later) gave +10%, then that way it's more of a "pick any 3 of the 4" to get 100% would be better. Or perhaps the +CR bonus should be part of the base skill without needing to be elite.
Missile Spec: Way too good. It increases missile DPS by a bit more than 65%, for one skill. For the player it's a capstone skill, but for officers it's basically just "another skill" once they reach level 4 without the attendant capstone tradeoffs. I think it should be more like +10% rate of fire, considering it already gives +10% damage, so you're still getting +21% damage which is still more than the other weapon skill bonuses (most of the time). Maybe +20% rate of fire.
Best of the Best: It's not so much "good" per se as that it's very generalist and "convenient" for just about every build, unless the player is trying to cap in multiple other directions, so it basically gets taken all the time. Pretty much every fleet can use being able to deploy more ships at start and a 3rd s-mod on every ship. Basically like the ITU of capstone skills. I'd switch some of its bonuses around with Hull Restoration (more on this later).
Support Doctrine: Interesting skill, I think it's fine where it's at.
Neural Link: I haven't played with this. However, I'm inclined to say that it's likely a bit weak, because the ship gets the officer skills of the player character, and if the player is already getting the NL capstone, then I don't see that many skill points left over for both the fleet and the player's flagship(s). So I would say, Neural Interface/Integrator should be decreased in cost, Integrator especially. But that's from looking at the skill effects, not personal experience. I'm sure people who have played with it more can give a better perspective on how its power is relative to the other capstones.
Automated Ships: I've only dabbled in this so no strong opinions on this. It depends on how much the automated ships are stronger than regular ships by enough of a margin that it's worthwhile to get this capstone.
Hull Restoration: The bonuses look useful if you're just starting out and don't have your economy set up, but basically not worth it for endgame fleets. So basically, pretty weak. Take at beginning and then respec once you can make enough money if you want to use it.
Derelict Operations: I think the biggest issue is that it *can* be powerful if you're lucky and get the "right" d-mods, but if you just load up on random d-mods, there's basically no net benefit between more d-modded ships vs fewer pristine ships (since some of the d-mods can really hurt). So you have to play d-mod roulette and hunt down the "right" d-mods, whether that's from letting your ships die or (more intelligently) check the d-mods on the ships you can loot/buy until you find the "right" combination. Someone proposed somewhere to allow the player to s-mod in their d-mods, i.e. make those d-mods unremovable from restoring, and I think that would be great for making DO more useful.
So my thought is this. BotB is too "convenient" while HR is too weak. To me, Leadership conveys better officering, crew morale, etc., which should mean the bonuses should be more about CR. While Industry is about the actual physical ship. Then why not switch those bonuses around? It's odd that BotB gives a 3rd s-mod (i.e. being able to make the physical ship itself stronger) while Hull Restoration gives +CR (which abstractly conveys crew ability), when it seems thematically like it should be the other way around.
I would say, have BotB give the deployment bonus and the +5% CR per s-mod, while Hull Restoration gives the 3rd s-mod instead of +5% CR per s-mod. That conceptually fits better with what each skill tree is supposed to be about, and splits up the "overly convenient" benefits of deploying more ships and an additional s-mod into different capstones.
If Crew Training were changed to +10% CR for all ships (instead of the current +15%), then this means that you can get to +100% CR by taking BotB and each ship then taking CE
or elite SE, or by each ship taking CE
and elite SE but frees up a capstone so that you can get Hull Restoration so all ships can get a 3rd s-mod. (I assume the player still takes Crew Training in either case.) Or, you just accept have 90% CR for that 3rd s-mod. Then it really *does* make it an "interesting choice" of would you rather have more to deploy at the start and CR, or a 3rd s-mod plus side benefits.