I’ve never done it, but these are my first thoughts.
what gearing does the F250 have? Make sure they are matched. You will probably be into re gearing one or the other. I’m assuming the 250 is not 4.10
Front wheels will have to be changed, or carry separate spares. I don’t know what you’re into to make them fit. Spacer / adapters...??
Brakes I’m assuming will all work, might just need to change lines to get everything to match up
Im also assuming long bed to long bed or short to short? Moving the flares to the 250? Fair job to get everything lined up properly etc, painting to match. That’s assuming you can’t simply use the 350 box, and happen to have matching colored boxes etc etc.
Id also look into the spring perches, spring hangars etc. Make sure they all match up. They probably do. If you’re from a rust belt area, make sure you can get the spring bolts out. You might be into cutting them, they do get seized in the bushings. You will probably want to take the time now while it’s apart and re bush the springs and shackles etc if they are 14 years old or have been worked.
As Mattman said, you will still be limited to what the truck is rated for.
Sounds like a fun project, but fairly involved for not a lot of gain imho.
One last thought on the off chance... I’ll also assume this isn’t a chassis cab someone mounted a box onto.