Sanity.
I mean fallout is a NUTZ world, you kill people, you kill monsters. People living today would go insane just seeing a super-mutant or a death claw. Not to mention the extreme depression that would happen a world as broken as Fallout.
I couldn't say exactly HOW it would play out.
Perhaps a reduction in certain skills or other stats related things. It could also play out in dialog and have an impact on your reputation.
Think how radiation works, something that's a rather long-term thing to worry about, but if you don't do anything to handle the problem it will become more serious.
Thoughts?