What actual devices did you use?
The same manufacturer (Hanna) of both devices (their digital refractometer in Rev's first post here and their inexpensive conductivity meter) claims the conductivity meter is more accurate (which presumably includes repeatability as part of that specification)
My Orion Model 128 conductivity meter COULD NOT be calibrated, so it never took any time to calibrate. Over the nearly 20 years I used it, it never drifted MORE THAN THE EQUIVALENT OF 0.2 PPT, and never needed cleaning. imo, They only need cleaning if you leave them in the tank water 24/7 (I do not advise that). An RO/DI rinse after each use precludes any need for maintenance.
I will say I am not a fan of conductivity probes on aquarium controllers that are left in the water 24/7. For whatever reason, that seems to lead to many problems.
I do also think it worth upgrading from the cheapest conductivity meters like the Hanna 86822 to better quality devices (like used Orion models on ebay with 4 electrode probes).
FWIW, I've seen quite a few folks complain about accuracy of the Milwaukee digital refractometer.