Same airline had a second Boeing 737-800 report a hydraulic failure the same day, which is why they're inspecting all planes of this type in South Korea. But it surprises me that no other country or airline is conducting any kind of safety check, even on a small sample of aircraft.
The sequence of events seems to be roughly this:
1. Hydraulic power was lost.
2. One aircraft made a successful emergency landing. The jet that crashed failed on first attempt.
3. On second attempt, all power was lost, resulting in no capacity to deploy flaps. Thus suggests the power loss is a result of slow damage caused by hydraulic loss, but we won't be sure until investigation is done.
4. Plane landed third of the way down runway and skidded into concrete radio beacon and mound.
5. Black boxes severely damaged by crash and explosion.
The black boxes are in an unknown state, as they're going to be electronic and there was no power. We have no guarantee that they will reveal anything after that power loss, even if the data survived.
My guess is that the investigators will find more on the plane that survived. There's not much info on it, but if the power lines were damaged when the hydraulic system failed, that might tell us a lot more than the exploded plane can.
But because it didn't explode or crash, I'm not sure if it'll be part of the investigation or merely repaired. I'm firmly convinced that the decision on this aircraft will prove critical.
The concreted radio beacon is considered safe, as that's the wrong way to land on that runway, but I'm unclear from the reports what, precisely, it is an aid for. If you just want a radio beacon, place the circuit below ground in a concrete box and have just the aerial on the surface. Colliding with an aerial is less likely to be dangerous and underground circuits will be easier to reach and subjected to fewer climate stresses.
I don't think they could have easily stopped the plane, but I'm unaware of any effort to dump fuel or otherwise lessen the risk of fire. If such measures were taken, they're not being reported.
The failure of two different systems also tells me that there's no redundancy and that both systems occupy the same space in at least one point, possibly along the same ducts. There's just about no other way the failure of one could cause the failure of the other.
The pilots did not follow the recommended remedial procedures for electrical failure, according to aviation reports, which might suggest they knew the system was fubar, but they might also have been too busy.
We will know more later, obviously, but I would be very cautious of Boeing 737-800s if they're not being inspected anywhere else. Until we know what the fault actually is, assuming it is local to one carrier in one country, where said country is good on aircraft safety checks, is probably risky.