We focus on two classes of organic switches operating due to the photo- or field-induced proton transfer (PT) process. By means of first-principles simulations, we search for the atomic contacts that strengthen diversity of the two swapped current-voltage (I-V) characteristics between two tautomers. We emphasize that the low-resistive contacts do not necessarily possess good switching properties. Very often, the higher-current flow makes it more difficult to distinguish between the logic states. Instead, the more resistive contacts multiply a current gear to a larger extent. The low- and high-bias work regimes set additional conditions, which are fulfilled by different contacts: (i) in the very low-voltage regime, the direct connections to the nanotubes perform better than the popular sulfur contacts, and (ii) in the higher-voltage regime, the best are the peroxide (-O-O-) contacts. Additionally, we find that the switching-bias value is not an inherent property of the conducting molecule, but it strongly depends on the chosen contacts.