1. you can't calibrate the digital sensor - as the name says it is digital and already pre-calibrated from the chip-vendor
max. deviation is 0,5°C

2. you can calibrate the analog sensor - or better: you calibrate the analog input port of the ProfiLux input probe
BTW: 677/319 are the standard values - I doubt that this is the specific calibration of your ProfiLux
to recover your calibration values from factory perform a "calibration" on the device itself (see manual)

3. I would trust the dig. probe

4. "The result is 10.3 degrees Celsius for the analog probe and 6.3 degrees Celsius"
This is outside the allowed measurement range for aquariums and means nothing (range min. is about 15°)

5. you can always use the "adjust temp." feature if you don't agree to the readings

6 "The analog probe is old for 6 years and the digtal one is new and faulty, which is a disaster for me."
If you are convinced that the probe is faulty and it is a disaster for you I recommend to consider a new probe