Full loop injection gives the best precision compared to the other injection modes, pretty much regardless of loop size. However, for smaller loops the overfill factor is larger and smaller tubing ID means the process can take longer.
The difference between 10 and 20 uL precision is negigible although of course 10 uL compared to a 20uL loop will use half the amount of sample volume.
My question in return is why do you ask? Are you seeing a difference?
I would go with the 10ul full loop max if using UPLC columns, larger injection volumes often lead to more broardening and hence loss of peak height (Signal/Noise). If you use 20ul full loop with 4 x overfill you will need to use a larger syringe this means steps per ul are less than with standard syringe no real gain. Whats wrong with 0.1% to 0.2% RSD? These numbers are attainable even with partial loop!
If its outside of this look at signal to noise, integration, peak skewness and other factors that can effect reproducability. Some of these include column integrity, sample stability and solvent/buffer composition and stability.