Old OS maps (1:1250 1954) seem to confirm that the road is called Hardgate the whole way along, while Crathie Gardens West would be a substreet. The sign in the first image implies that the road is called Hardgate where the sign is, but the name changes to Crathie Gardens East some way along the road in the direction of the arrow. The house numbers on the east side of the road follow on from the other houses on Hardgate to the north though. My conclusion would be to change the road name to Hardgate, tag the houses on the west side of the road with Crathie Gardens West as addr:substreet, and ignore the Crathie Gardens East road sign. However I can see in the history that you changed the road name from Hardgate to Crathie Gardens East in the past, so since you've actually seen the road and signs in person what do you think would be the most appropriate tagging?