Why are multimeters much more sensitive than oscilloscopes?
if both are 12bit then, the DMM has a much smaller full scale reading , eg 200mV, 
whereas DSO might be 100mV/div .
10uA is not a suitable parameter for DSO's. 
If you wanted 100mV on DSO then Rs would be 100mV/10uA= 10k not 0.5k Ohm


Thus the problem may be your test method, not the instruments.