When the value of what you are locking up demands a higher level security. Think multi-thousand dollar e-bike, scooter or small motorcycle. Expensive generators are high targets as well. We consider a U lock to be High Security when the shackle is at least 12mm (preferably higher) and the lock is fitted with a higher level pick resistant key-way. A proven* test seal like Sold Secure helps to get our high level mark.
(* some brands stretch the truth on their test seal approvals)