The development of antibody therapeutics is a major focus in healthcare, owing to their high binding affinity and specificity. To accelerate drug development, significant efforts have been directed toward the design and screening of antibodies. For effective \textit{in silico} development, high modeling accuracy is necessary. To probe the improvement and limitations of AlphaFold3 (AF3), we tested the capability of AF3 to capture the fine details and interplay between antibody structure prediction and antigen docking accuracy. AF3 achieves a 8.9\% and 13.4\% high-accuracy docking success rate for antibodies and nanobodies, respectively, and a median unbound CDR H3 RMSD accuracy of 2.04 Å and 1.14 Å; CDR H3 accuracy also boosts complex prediction accuracy. Antigen context helps improve CDR H3 accuracy for loops that are greater than 15 residues long.