Hm. Spent a few hours with this. Combat feels a bit shallow at the moment but I'm sure that'll change. I really appreciate fleets auto micro depending on their make up (beamers move in close, missile ships stay at range).
More offensive diplomatic cards would be nice. Stuff like "enact trade sanctions" (reduces enemy empire's income) or "galactic war" (everyone declares war on an empire). Galactic Civilizations 2 has tons of stuff like this that might be worth a look.
FTL Energy doesn't feel restraining, at least with hyperdrives. I haven't messed around with the other drives yet. Maybe increase the default cost of using hyperdrive (and storage, to make it feel more strategic in use).
This is kind of a vague suggestion, but maybe to make combat more interesting you could scale down the fleets? Make them cheaper to upkeep and build, so that you'll have more operating at any one time. By midgame I had about 9 fleets, which was only enough for 2 task forces and maybe a defense fleet.
Also, it would be great if there was an option to auto rebuild support ships in fleets, maybe on by default.
Remnants feel a bit awkward right now. You can still colonize the system with them there, but they'll swat colony ships that pass over them, which causes problems later on. They're strong enough that you need a decent sized fleet to take them out, but the benefits (the little item you get) aren't that great. Maybe they could be support ships orbiting planets instead? That would block off colonization, making them a bigger threat, but also less dangerous as they wouldn't have a capital ship.
Bring back the rings from Star Ruler 1. The ones that showed military power. Those were great for seeing what was happening at a glance.