First of all I am NOT a NiCad expert but I am familiar with them as pertains to aviation use.
Pros - they have a very long service
life - if correctly maintained; they can be very deeply discharged without ill effect; they maintain a very stable voltage during high current
discharge and until almost fully discharged; they can be repaired (i.e. dead cells replaced); they have more capacity per size than FLA.
Cons - they are very very expensive; they don't like high charge rates (but can accept very high charge rates for a short time; they can suffer from thermal runaway and can be quite dangerous; they require regular servicing to maintain life and full capacity.
Having said that, most aircraft charging systems are basic and NiCads are usually charged at 1.7 V per cell. They will accept whatever current
is available (depending on their state of discharge but they can be damaged if charged at this rate when deeply discharged. In theory, they only need recharging after a start so discharge is not high, therefore charge rate is not too high from a basic regulator, the rest of the time they are floated. And they are regularly serviced by being completely discharged to zero capacity and then recharged at controlled current rates.
I am not sure of the advantages to be gained by using them as a house battery
(even if you have access to a smart current controlled charging system on board).