Several points to consider. At this size, anything above 1 litre, pot size is measured in volume, you will find this stamped on the base of the pot. If you tilt the pots over the details should be easily visible. This will help you understand how big a jump to make in pot size, I'd suggest at least doubling the volume, though it's difficult to tell from an image. You can also check by measuring diameter and height but this can be deceptive if the pots you are comparing have different profiles. I agree the smaller one can probably move in to the bigger.
Has the damage suddenly appeared this winter or has it been building up over a long period? My reason for asking is the last six months have seen unusual weather conditions, the result all over Lancashire, especially on the Fylde, is literally hundreds of dead Cordylines and to a lesser extent Phormiums. I appreciate these are palms but it could be the cause. The Cordyline I've seen are very mature plants, which we have come to consider hardy, that have suddenly succumbed to the weather. We had an unusually long, warm autumn and extended growing season, when temperatures changed quickly soft growth on these plants wasn't hardened off and sustained a lot of damage with far, far more death than I've ever seen. As one singe example I had a 15 year old Cordyline growing in container in the backyard, protected by walls on four sides, it's dead. Same in my garden, Phormiums which have been happy for years are dead.
Assuming cold isn't the problem I would suggest you have four issues to consider, overwatering (rain), lack of feed, frozen root system and after six years in these containers the plants are probably completely pot bound. Your first step should be to establish if the root system is still healthy, light brown to yellow and they are happy, mushy in appearance and touch and they're dead.
If you do repot go for a John Innes No. 3 compost or similar and pots with plenty of drainage. It would be worth drilling extra holes in the base and if you can raise the pot slightly off the ground. I'd reckon on a couple of hours to do the job.