To be fair, Lahabrea didn't really seem like he was going for the deathblow in that first fight. He did state his intent to kill, but he was hardly trying compared to his performance in the Aetherochemical Research Facility. Granted this can be chalked up to arrogance on his part and Hydaelyn Herself actively assisting us in that fight, but even so.
More to the point, the thing with Lahabrea (etc.) wanting more darkness and Elidibus trying to maintain the balance is a matter of perspective, I think. Lahabrea (etc.) wants to bring forth more darkness and chaos proactively - he's very aggressive with his strategies, trying to get as many Primals summoned and stir up as much shit as he possibly can. He was behind the Calamity in some way (apparently?), got the primals summoned, led the Rogue XIVth to refurbish the Ultima Weapon, helped them start a war with Eorzea, etc. They all seem to be actively trying to bring more chaos into the system.
Elidibus, on the other hand, is reactive and defensive. He prefers to negotiate and has only acted violently in defense (once, against Minfilia). That said, his comments on "balance" are likely something more like "The balance is shifting towards light, which is bad for our plans." He'd be perfectly fine with it tipping toward darkness, so it's not that he wants to maintain balance for the sake of having balance - the order we're bringing is just reducing the chaos, which is detrimental to the Ascians' plan(s). I'd say the Warriors of Darkness are here to screw everything we've worked so hard to accomplish up, but with only that brief scene with Darklander, I'm still not sure where their true intentions lie - much like Elidibus.