How do I know when concrete needs replacing rather than just mud-jacking?
The key criteria is how stable the ground beneath the concrete is.

If the ground is stable you can patch and mud-jack your driveway efficiently. Otherwise patches of any kind are a waste of time - after you patch the pieces won't be perfectly attached to each other, so they will come apart again in no time. If that's the case you have to remove the concrete, remove a layer of  ground beneath it, put a layer of crushed stone, ram the crushed stone thoroughly and then put the new layer of concrete. That will stabilize the ground and you'll have the driveway with decent lifetime.