Why doesn't small rural community hospitals keep up with big urban ones?

They cannot. Small rural community hospitals- staffed generally with general practioners, or internists without any sub specialities, surgery, or ob/gyn. They are not equipped with ct/mri, icus etc urban hospitals: most of them all specialists andp advanced medical equipments other resources that are essential for care of patients.
Depends. Most medical issues are fairly standard and can be handled well my community hospitals. There are certain procedures that typically need to be done in large centers. Also, complicated, nonstandard issues may need to be seen by a specialist. Besides those issues, most community hospitals are effective at treating most illnesses.