I suppose the best comparison for a GCIII space battle in SoaSE is if you were to play out a battle in SoaSE completely hands-off. The result of the engagement is determined by what you brought to the fight, and perhaps a bit by when and where you fought, but all it really offers you is a pretty light show. You arguably have a bit more influence over what you bring to the fight in GalCiv than you do in SoaSE since you can design the ships (in GCII and GCIII) and (in GCIII) set the role of the ship (which sets its dominant targeting priorities), but once the battle begins it's essentially a dice rolls + modifiers system which neither requires nor permits player influence. Note that although dice rolls are involved, the system is highly deterministic; if you bring a ship with 10 HP, 10 beam attack and 10 armor to a fight and I bring a ship with 10 HP, 10 beam attack and 10 shields to a fight, there is a very high probability that I'm going to win and you are not (and even moreso in GCIII than GCII; off-type defenses provided some protection against attacks in GCII but do not do so in GCIII).
Regardless, GalCiv is not a game series that I would recommend on the strength of its space battles. In fact, if interesting space battles are what you're looking for, I'd strongly recommend looking elsewhere, as at least in my opinion the battle viewer is entertaining only the first time or two you watch it, and maybe once in a long while afterwards, and unless you're playing on a fairly small map getting to the point where you have space battles can take a lot of time unless you count fighting pirates. If space battles are what you're looking for, then I'd recommend games like Gratuitous Space Battles or its sequel (slot-based ship design, hands-off battles that are however strongly influenced by the player due to the ability to set standing orders for each ship you deploy in the engagement; sequel is more or less the same but has more visual customization available for the ships, though this doesn't affect ship performance), Sword of the Stars (ship design similar to Gratuitous Space Battles, ships are mostly player-controlled during the battles though you can allow them to act on one of several stances, and is a reasonable introduction to turn-based 4X strategy; the sequel was somewhat interesting but overall disappointing and I wouldn't recommend it), Distant Worlds (ship design somewhat similar to GCII/GCIII but in an RTS game sort of like Sins of a Solar Empire with a far more detailed resource model; the game is also somewhat expensive and some people may take issue with the graphics), or Empire at War (mostly analogous to SoaSE, though planets are more customizable and research is much less of a thing); I've also heard good things about Homeworld and its sequel, which were re-released recently as a package deal with improved graphics, though I've not played either.
What GalCiv does do is empire management. You decide what gets built where on each of your colonies (though you can, as of v1.3, allow the computer to do this for you), set certain planetary expenditures (not as freely in v1.4 as in earlier versions, though it sounds as though they may be reverting that change and instead introducing a penalty for focusing too heavily on any one output in an upcoming patch; as with the other part of colony management, this can be handled by the computer if you want), choose how many and which ships are built and where, the composition of the fleets you'll field, and the designs of your ships (as with colony management, ship design is optional; the designs you'll get if you allow the computer to handle ship design are about on par with what the computer-controlled factions will have, which is to say mostly adequate but not great and usually not really ideal for whatever you're facing). GalCiv is much more of a building and management game than it is a space combat game; what interest it offers by way of its combat system is almost entirely in the strategic aspects of where and when to fight, and how to position your forces to allow you to control that, and also a bit in what forces to bring to ensure the greatest chances of victory. Otherwise, GalCiv's combat system is a choice between a fast and a slow autoresolve, with the fast autoresolve letting you get back to the main part of the game sooner and the slow autoresolve showing you essentially the same battle every time you choose to watch it, which might be entertaining every once in a while but isn't something that I usually bother watching.
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