The aggregation of amyloid-β (Aβ) and human islet amyloid polypeptide (hIAPP) proteins have attracted considerable attention because of their involvement in protein misfolding diseases. These proteins have mostly been investigated using atomic force microscopy, transmission electron microscopy, and fluorescence microscopy to study the directional growth of fibrils both perpendicular to and along the fibril axis. Here, we demonstrate the real-time monitoring of the directional growth of fibrils in terms of activation energy of proton transfer using an impedance spectroscopy technique. The activation energy is used to quantify the sensitivity of proton conduction to the different stages of protein aggregation. The decrement (increment) in activation energy is related to the fibril growth along (perpendicular to) the fibril axis in intrinsic protein aggregation. The entire aggregation process shows different phases of the directional growth for Aβ and hIAPP, indicating different pathways for their aggregation. The activation energy for hIAPP is found to be smaller than the activation energy of Aβ during the aggregation process. The oscillatory behavior of the activation energy of hIAPP reflects a rapid change in the directional growth of the protofilaments of hIAPP. The results indicate higher aggregation propensity of Aβ than hIAPP. In the presence of resveratrol, hIAPP exhibits slower aggregation compared to Aβ. Methods of this study may in general be used to reveal the modulated aggregation pathway of proteins in the presence of different ligands.