Mrs B says... supposing she dialled 999 from our landline, the dropped the phone down the sofa (or whatever) could the police trace the call more easily than from a mobile?
They can accurately trace a phone in the same way your phone can let you know your GPS location. So basically, they can find what street you're on and even what shop you're out side of.
You should watch some 999 programs on TV when they call up, the first thing they do is find a location and they do this very quickly.
I would say a landline is more accurate.. Only because it's hard wired into the wall of the house.
BB, if you call the police, and just breathe down the phone, or for example press the number 5 on your phones keypad, they will be able to track the call and they will still send someone out.