They are easier to tune, don't have neck dive, and reputedly have fewer dead spots on the neck. I say reputedly because my only headless is a Steinberger, which has no dead spots, but the design is so radical that one cannot solely credit the headlessness.
The advantages are real, but not earth-shaking, so a lot comes down to personal taste.
Status Stealth 5 => EBS HD350 => EBS Neo212
Steinberger Club #0013, Pedulla Club #147, Pre-EB MM Club #44 , Epiphone #90, EBS #34