I would characterise them this way:
"getting on" means, making progress
The word "just" would indicate a negative tone. Just making progress.
"fine" means, ok or satisfactory or acceptable.
Please keep in mind that one persons use of the word fine may differ from another person because everyone has their own criteria of what level of performance would be fine verses bad or good or great or even getting on.
Which is better? Is it better to make progress or do satisfactory? One could argue both sides. Its in the eye of the beholder, or subjective. Both are general terms, maybe ask him for elaboration?
The word "just" in "just getting on" shows a little negitivity. Thats how I look at it, I am sure others may see it differently.