Remeber, not every locale is the same.
Our local 911 area goes to the county 911 center, so it's as fast as land-line 911.
Also, our 911 center handles 4 towns EMS, their PD's and county sheriff. The city PD we live in only answers calls from 8am to 5pm / Mon. to Fri. and doesn't do dispatching. So any other time it goes to the 911 center anyway. We always dail 911.