Depends on the circumstances. If you have a good source of clean cardboard that can be easily shipped to a recycling plant the economic value of the cardboard can certainly be higher recycled vs burnt.

Let the market decide.

Note that one consideration is recycling cardboard mixed with plastics is definitely a microplastics hazard as it produces a lot of microplastics contaminated wastewater. If you just incinerate it properly, you eliminate that hazard. Some uses of cardboard for packaging have a lot of plastics mixed in; others do not. We might be better off eliminating consumer paper recycling in favor of incineration, and allowing more controlled recycling (eg boxes from wearhouses) to continue.

...and yes, in general we should be using incineration a _lot_ more to fully eliminate plastic waste rather than leave it for a future generation to deal with.