Yes that is similar, in that all networks require the remote end to be working. The difference/s between the PSTN network and the NBN are a few. Depending on the technology in an area there may be several places where a power failure could affect usage. Let's look at your Wifi tower compared to your old wired connection.
Points of possible power failure interruptions
The Node (Collector where multiple connections come together and this could be the exchange or POI)
The POI (if not already the Node)
Next we can look at FTTN
The Mini Node (if you are unlucky to have one)
The POI (Exchange for easier explanation)
The Cable power supply (usually at the poles)
The Node (yes they to have a node)
Satellite (if not using the old copper)
The Satellite (this would be a big issue)
The POI power supply is pretty solid, it is like the old exchanges and in many cases are the old exchanges, they have multiple backups including Generators and Battery banks. Likelihood of failure is very low unless catastrophic failures occur eg Floods, or Fires within the exchange.
FTTN Cabinets (Nodes) are being fitted with 3 backup batteries but the NBN state not to trust that system but up to 4 hours may be expected. They are also generally in relatively close proximity to your premises and are easily affected by floods if in low lying areas. Also affected by lightning strikes. The remaining copper lines to your premises can also be affected by water in the pits and pipes just as your neighbour experienced on the old PSTN network
Mini Nodes do not have backup power and fail if no power in the area. They also are compromised by water inundation and lightning damage. And again the remaining copper wires may be affected by water in the pipes and pits.
HFC (Cable) has no backup power and so like Mini Nodes in power failures they cease to operate. The pole or ground nodes if flooded cease to work. Lightning strikes can be an issue. If underground cable the pits and pipes flooding is also an issue
Wifi Towers have backup power again good for around 4 hours maximum and again no warranty on that as my mother experienced. Lightning strikes can be an issue. Cyclones and similar strong wind events can destroy or badly damage the tower.
FTTP only requires power at your house and the POI. Works even when flooded, does not corrode, non conductive so resistant to lightning damage. As most of the FO infrastructure is underground it is largely protected from wind damage.
The risk of failure for most of the NBN technologies is much higher than that of Fibre to the home and Fibre to the home is less likely to have failure than even the PSTN system. Satellite is a problem not so much because of power but because of weather conditions as @gordon can attest to.
In floods the copper circuit, whether it was/is on the PSTN or as part of the MTM NBN, is easily compromised by water and if you are likely to have your copper connection affected by floods either at your premises or between you and the exchange then yes a mobile is a sensible precaution.
The NBN has done risk analysis and has told us that we should have a mobile ready in case of failure particularly if we require uninterrupted communications, they are not requiring or demanding that we get a Smart Phone or some expensive model. They have said they cannot guarantee us service and they are telling us a mobile phone is a precaution to take just like people who live in areas affected by Cyclones who are advised to have torches, batteries, a portable radio, potable water etc ready for the storm season.
A site where you can check and comment on NBN Outages:
From the NBN Statement of Expectations:
"Communicating and managing risks
The Government expects that nbn will actively manage risk. It should communicate risk to Shareholder Ministers and Departments, and engage closely with them, including by providing monthly progress reports. The Government expects that nbn will continue to strengthen its engagement with Government agencies. This should include security agencies to address security risks related to the network."
From the NBN Co site re Emergencies and outages
What to expect in an emergency
Equipment connected over the nbn™ network will not work during a power blackout.
While nbn will endeavour to get our network back up and running as soon as possible, you should be prepared to be without internet and telephone services for a period of time.
An emergency may trigger a power outage. If you require a safety critical device such as a medical alarm, fire alarm or lift emergency phone to work during a power outage, nbn recommends that these should be connected to secondary communications technology such as a mobile network connection or battery backup. You should make enquiries about the operation of these safety-critical services during a power outage with your device provider or your phone or internet provider.
Prepare an emergency kit
We recommend that you put together an emergency kit, which includes equipment that can be used in the event that there is a power outage or your connection to the nbn™ network is disrupted.
Equipment connected over the nbn™ network will not work during a power blackout. Electronic equipment connected to the nbn™ network needs its own separate battery backup to work in a power outage. Examples of devices requiring separate battery backup include your modem, cordless phone, gateway or WiFi router. This is not provided by nbn.
A number of factors influence the resiliency of the nbn™ network to continue to provide uninterrupted services during a power outage. Even with network power resiliency and in-premises battery back-up, power outages may last longer than the battery life. Therefore, we recommend you are always prepared to be without internet and telephone services for some time.
nbn™ network outages
Unplanned or unexpected outages to your nbn™ network connection can occur for many reasons, such as severe storms, cyclones, bushfires, car accidents, or trees or branches falling onto power lines.
nbn understands the inconvenience unplanned outages can cause to users. This is why we have an emergency response team dedicated to preparing for and responding to the recovery of the network in emergencies.
We have worked with local authorities and emergency services to identify high risk areas and buildings of importance like hospitals. We are constantly working to make sure our network is as resilient as possible, undertaking work such as vegetation clearance around sites in high risk bushfire and cyclone areas, checking seals on cabinets in flood prone areas and the stocking of operational vehicles with the agreed levels of network spares along with the required tools and equipment in order to respond to emergency events.
Where possible, nbn will deploy temporary network infrastructure into areas where extended outage durations are anticipated. This infrastructure is designed to provide temporary services to support emergency services and the community and its allocation will be based on the network infrastructure available and be on a best efforts basis."