Damaged clothing is less warm, and less protective.
Damaged weapons are less accurate and do less damage IIRC. Damaged guns are more likely to jam.
Damaged vehicle parts perform worse: tanks and batteries leak, solar panels produce less epower, engines consume more fuel to produce less power while making more noise, etc.
For just about every item, damage reduces functionality and you’re usually better off using a weaker, fully repaired item than a better heavily damaged item.