Personalised attention and Chaos or Standardization and Stability ?

Chris Alcock ( Master Black Belt ) asks this question :
Would you rather me go the extra mile for a patient or follow a good process?
 
https://www.theguardian.com/uk-news/2017/feb/09/nurse-spared-jail-after-fatal-blood-transfusion-mix-up
I know which sounds better, but which would you actually rather have?
Good healthcare by dint of extraordinary effort?
Or a process that leads the nurse or doctor to the most accurate and fastest outcome most of the time?