In practice, there is no difference in how you adjust the compensation of the probes - regardless of which "end" the adjustment capacitor is on. It's just a difference in the internal construction/design of the probe.
As for the broken probe - look like maybe the internal 9M series resistor may have opened up. You can try to repair it, or "glue" the switch in the 1X position and only use it for those infrequent applications where a 1X probe is appropriate.