It is depends on ELISA test . Usually, ELISA test protocol contains information how plasma samples should be prepared to the analysis. Sometimes both EDTA and heparin vials are compatible but sometimes not. You have to check your ELISA test protocol.
For oxytocin and vasopressin which are small and fragile peptides, I would recommend you tu even use EDTA-Aprotinin tubes to take blood samples. Aprotinin is a protease inhibitor which can help prevent these neuropeptides from degradation, as well as pre-chilling your tubes and keeping them at 4°C until centrifugation. Pre-analytical treatments are crucial steps to ensure valuable measurements.