The difference is to do with returns to scale. So if you go for the CCR model you are assuming constant returns to scale so a doubling of your inputs ( age, weight, height and type of work ) should result in a doubling of the outputs ( performances in physical activities, squats and endurance. ) this is not what you want!

But note that although the BCC model is variable returns to scale it still expects an increase in input to be associated with an increase in output, just not in a linear way. This is also unlikely for your data as your inputs include age (and i suspect that while a 18year old can do more squats than a 1 year old, a 95 year old will do less than the 18 year old!).

Type of work is clearly not a ratio type variable and so will need special encoding etc.

Similarly you will need to consider what variable you use to describe " performances in physical activities" while more squats and heavier weights lifted are better performance, for time to run 1km lower times are better.

You might find the following paper useful in thinking about some of these issues Article Applying Data Envelopment Analysis to Preventive Medicine: A...

In your case based on the the type of variables you are taking, it seems that you should use BCC model.