I think the way people experience particular illnesses and symptoms vary so widely, both in how their bodies respond to a disease/injury and how they cope with what they experience, that it is impossible to say that NTs on average experience illness differently from ND people on average, there's just far too much in-group variation.
Just take how differently people respond to colds. When I get a cold I am out for the count, I feel extremely ill, achy, dizzy, exhausted, unable to concentrate, my nose runs constantly (I will get through 5 boxes of tissues a day), I am literally unable to work. My mum is the same. Meanwhile some people get a mildly sore throat and sniffle a bit and can go about their day as normal, with exactly the same virus, my dad and sister are like that. (for context, my mum and sister are NT, my dad and I are aspies).
On the other hand I cope with pain very well, I live with chronic back and ankle pain and it doesn't have any particular negative effect on my life, aside for an inability to run. I have been extremely prone to tonsillitis and ear infections since I was a small child and so I barely notice these illnesses even when they are very painful, while other people with minor symptoms will go straight to the doctor for antibiotics and take time off work.
The only way I can imagine any real difference is the potential for the symptoms to become overwhelming leading to a meltdown/shutdown.
One thing I have noticed, when I'm running a fever I suddenly become extremely touch sensitive, even to the point that I can't bear to have clothes on me, not sure if this is something that NTs also can experience?
It's not universal but isn't an uncommon experience. My (NT) mum experiences this, as did my Gran. Mum has silk pajamas specifically for when he has a temperature because it's the only material she can tolerate.