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Most glues are capable of bonding 2 pieces of cardboard together and so it is more then a matter of application and thickness of the cardboard - the thickness will effect the weight and so the forces that the joint will need to hold.
For cardboard models where you will be forming 3 dimensional joints and you will have a tendency to put quite high forces onto the joints as you pull the model into shape then a good glue is a PVA or an Aliphatic. The glue stick is not really suitable as it has a tendency to go brittle and lose strength over time.
This type of glue is fine for paper and thin cardboard, but the strength of the joints tends to be low and so not recommended for joints that need to take load.
A plastic usually abbreviated as PVA. A colourless transparent solid, it is usually used in adhesives, which are themselves also referred to as PVA or PVA adhesive.
The main benefit of this type of glue with cardboard is that it forms a very strong joint and is easy to use.
As cardboard is porous the glue will seap into the cardboard and can discolour it - you can overcome this by using the glue sparingly.
Also, this glue is slow drying and so you will have to leave the glue to dry or apply a clamp to hold the parts together whilst you continue to work.
This is not exhaustive and so please do email me if you have a question or even better an answer.