Antibodies are the most important reagents for the development of highly sensitive and specific immunoassays to quantify analytes of interest in food and environmental samples. While immunoglobulin G (IgG)-derived antibodies from rabbit and mouse are traditionally employed in immunoassays, recent findings suggest that chicken egg yolk antibody (immunoglobulin Y (IgY)) provides several advantages over mammalian IgG. However, limited studies to date have examined the possibility of replacing IgG with IgY in immunoassays. In the current investigation, the performance of chicken IgY and IgG derived from rabbit and mouse was systematically compared in terms of sensitivity, specificity, and matrix effect under parallel conditions with three typical assay formats, specifically, indirect competitive enzyme-linked immunosorbent assay (icELISA), fluorescence polarization immunoassay (FPIA), and colloidal gold immunochromatographic assay (GICA), for detection of sulfamethazine (SMZ) as the reference molecule. We evaluated and discussed the influence of different coating antigens, tracers, and physicochemical factors on the performance of IgY and IgG in the immunoassays. Under optimized conditions, the sensitivities of icELISA (IC50 values of 6.70, 4.76, and 1.66 ng mL−1 with recoveries of 86.1–131.8% and precision of < 12%) and FPIA (IC50 values of 24.79, 20.87, and 10.83 ng mL−1 with recoveries of 81.8–120.2% and precision of < 17.3%) based on both IgY and IgG were sufficient to detect SMZ in milk while only GICA based on mouse IgG provided acceptable sensitivity. Our collective data indicate that IgY could be an acceptable alternative to mammalian antibodies in some situations (in icELISA and FPIA) for use in the development of effective immunoassays for screening and detection of veterinary drug residues in food samples.