Hi -- Generally category C & D write offs are easier to repair, depending on age a category D might be nothing more than a keyed panel. but a category C needs an ID check before going back on the road.
If you're buying a category C you should be asking how come it was viable to repair contrary to the category & what damage it sustained, can you see photos to verify what that damage was, who repaired it, also it should have undergone a VIC (vehicle identity check) by VOSA, once it has passed... the DVLA then issue a new V5 regisration document.
Generally speaking a category C write-off is one where the cost to repair was more than the value of the car.
A category D write off is where the cost of repair is more than 60% of the value of the car. Insurance companies tend to write them off above this figure to avoid nasty shocks.
Some insurance companies will not cover category C or D cars - I think it's because their value is lower by virtue of their history and it complicates things if they have to pay out on them. But there are plenty that do, bear in mind though the car will always attract a lower payout from the insurance if written off due to it's decreased market value and past history.