When wearing/ using 24/7... No different when sick! Just as using the bathroom can be a necessary inconvenience, so can diaper changes. However, diaper changes can be less frequent than using the bathroom with a good diaper, assuming one of your symptoms isn't loose bowels - those are the worst with diapers and often require multiple cleanups (shower easiest) in short period of time. Haven't had messy diaper blowout recently when that's happened, but it's a possibility if you don't change expediently! Not to mention the sometimes acid stuff against your skin...
Also, diaper changes have less urgency - you can wait to some degree until it's more convenient (your fever breaks, your head stops pounding as much, etc...) to change your diaper - you can't really wait out strong urge to use the bathroom.