I think there will be a massive difference between imperial and hive worlds as to how a natural disaster is dealt with. I'll give a few scenarios and then how I feel the two world types would respond:
Hive worlds will suffer far worse if an earthquake of a serious magnitude were to strike a major hive due to the centralisation of citizens and industry however it can be assumed that the hive structures will either have anti-quake tech in their construction (similar to modern day skyscrapers, especially in Japan) or just be so bloated that a quake would simply cause a few layers of the hive to cave in and provide a steady surface for those layers above. That said a truly major earthquake (and cause this is sci-fi we can assume they would be capable of going off the charts we use on earth to gauge them) would be capable of levelling an entire hive city and thus all but annihilating the planets population and infrastructure. Arbites, PDF and any other forces on the planet would be used to clear wreckage and rescue workers, assuming any survive billions of tons of rubble and wreckage collapsing on them, but for the most part I’d imagine the hive and potentially the whole planet would be a write off.
Imperial worlds would fair better with earthquakes due to no centralisation of industry or populace. Whilst key areas might be struck and the losses in life and infrastructure could be high, the planet would likely be able to adapt and continue in whatever purpose it was configured for. As with hives any local forces would assist in clearing and search & rescue operations, and chances are there would be less to clear and more to rescue than a hive.
I see hive worlds being far better at coping hydrological disasters such as tsunamis – often they are on arid worlds where ocean levels have long since dropped due to heavy industry. Those with large bodies of water indeed often have water-borne hive cities with unique adaptations and technologies to help them cope with tides etc. Even if a large tsunami were to strike a hive city I feel it wouldn’t do much more than flood the lower levels, in fact cleansing them of a lot of the built up filth. In the long run there might be issues with subsidence but for the most part the lowest levels of hive cities are not where productive citizen workers and the profitable industries are based. There’s not much that local forces would be able to do to help clear the flooded levels or rescue anyone however so I’d imagine the losses in affected areas would be almost 100%, however they would be useful in putting down any riots that arise from the tsunami.
Imperial worlds on the other hand are likely to fair worse due to infrastructure being spread out. As these planets are often used for their agriculture, mining and crafting trades then these are likely to be hit harder as vast swathes of industry and population are swept away or at least interfered with by the flooding and waves. That said any local forces would be able to use vehicles and aeronautica to assist in clearance and search & rescue quite effectively.
Hive cities are often centres for production and make use of geothermal resources in their industry. As such any volcanic activity could prove disastrous to these hives perched on top of an active volcano. That said it could be assumed that there is some sort of technology that can either block any eruptions or shield the hive itself. Any areas that were affected would be unsavable however as entire levels of infrastructure and population would be incinerated and trapped. As such local forces would be of little to no use except in running crowd control to keep the masses from rioting.
Imperial worlds would once again fair better with volcanoes due to their spread of infrastructure and populace. Depending on the tech level of the planet it might be that with enough warning there could be full evacuations of the affected areas, or could be that local forces be brought in to keep civilians from panicking and causing further issues to the infrastructure and populace. This is probably one of the harder ones to comment on due to the diverse nature of imperial worlds
This one should be really simple to analyze so I’ll do so in a single paragraph – Hive worlds have far too dense a population to easily stem the spread of plagues or diseases and so although some of the rich nobles in their upper spires may be able to affect a quarantine or afford medication and treatment, for the most part the majority of the population is utterly screwed. If the health disaster is a fatal one this could lead to ghost-hives as entire populations are wiped out. Imperial worlds with their diffuse populations should fare about as well as 19th and 20th century earth – the poor may well suffer, but for the most part epidemics can be contained and treated. Local forces would be used for quarantines and removal of the dead in both world types.
These are largely of two types – impact events and gamma-ray bursts and solar flares.
Impacts would affect a hive far worse than an imperial planet but only if they struck directly. Small impacts might only affect outer hive layers or be repulsed by shielding but a major impact event would just annihilate a hive city. An imperial world might be able to survive bigger impact events due to its diffuse population and infrastructure and local forces would be of more assistance in the aftermath.
Solar flares would need to be massive and the planet close to the star in its system to have much effect, though I’d imagine hive cities would be better shielded due to their structure and often having actual shielding. On the other hand their technology would be far more screwed so it could swing either way really. Imperial worlds again would fair better and often have a lower-tech infrastructure. Local forces might be able to operate using hardened, reliable military hardware but also might not!
Gamma-ray bursts would be devastating to a planet regardless of its type, though the more advanced hive planets might have some ability to withstand minor bursts. Now I’m not a scientist but as per Wikipedia it states that extended gamma-ray bursts could lead to depleted ozone layers, mass extinctions, food chain depletions and starvations. Long-term effects could include photochemical smog and darkening due to block light, which in turn would lead to further depletion of the ozone layers. Whilst imperial worlds would be devastated by these affects, hive worlds would at least already be adapted to smog, darkening, lack of ozone etc. Local forces wouldn’t be able to do a thing about this event type other than prevent rioting due to starvation etc.
Imperial worlds will be more screwed over by severe avalanches, with entire communities being crushed and cut off. Local forces would actually be quite useful in these situations as long as they had the correct equipment to clear anyone or thing trapped by the avalanches.
A Hive world on the other hand would be largely immune to avalanches as hive cities are so vast and sprawling that I can’t comprehend a scale of avalanche that could smother a hive city. Lower reaches could get blocked but a if a hive city was on a planet known for avalanches and in a location near mountains then it would have enough industrial gear to hand that it shouldn’t be much of a problem.
As imperial worlds often make use of extensive farmlands and other arboreal regions any scale of wildfire could be dangerous. Local forces would be paramount in combating these fires in addition to any civilian agencies that might exist (40k fire-fighters must be hardcore and I want to see them covered somewhere!).
Hive worlds will be less susceptible to wildfires as they are almost never surrounded by viable soil for any sort of flora to grown in. It could be however that a hive had its primary food sources cut off which could lead to starvation or drop in off-world exports, so local forces would once again be paramount to dealing with any fires.
Including blizzards, cyclonic storms, droughts, hailstorms, heat waves, and tornadoes.
Imperial worlds would be about as affected by these as modern day earth would be so I won’t really go into them.
Hive worlds I would imagine would be largely immune to most of these affects, the exception being heat waves. Whilst blizzards, hailstorms, cyclonic storms and tornadoes may batter the outer layers of hive cities, their tremendous size and shielding would protect the contents of the hive from the worst of these. Local forces might be needed to dig out some out of the outer layers that become clogged or collapsed however. Droughts will largely be overcome because the majority of hive cities import the essentials such as food, water and sometimes even clean air. Heat waves however could lead to significant deaths of citizens or damage to machinery, unless the hive was situated on an arid or hot world where sufficient cooling was built into the hive.
These are all just my thoughts and opinions on the various threats and I apologise that my short answers turned into a 1500 word essay but once I started I found I couldn't stop!