Brain function does not emerge from isolated activity, but rather from the interactions and exchanges between neural elements that form a network known as the connectome. The human connectome consists of structural and functional aspects. The structural connectome (SC) represents the anatomical connections, and the functional connectome represents the resulting dynamics that emerge from this arrangement of structures. As there are different ways of weighting these connections, it is important to consider how such different approaches impact study conclusions. Here, we propose that different weighted connectomes result in varied network properties, and while neither superior the other, selection might affect interpretation and conclusions in different study cases. We present three different weighting models, namely, number of streamlines (NOS), fractional anisotropy (FA), and axon diameter distribution (ADD), to demonstrate these differences. The later, is extracted using recently published AxSI method and is first compared to commonly used weighting methods. Moreover, we explore the functional relevance of each weighted SC, using the Human Connectome Project (HCP) database. By analyzing intelligence-related data, we develop a predictive model for cognitive performance based on graph properties and the National Institutes of Health (NIH) toolbox. Results demonstrate that the ADD SC, combined with a functional subnetwork model, outperforms other models in estimating cognitive performance. Author Summary This study compares different approaches of weighting connections in the human brain structural connectome. The three chosen methods for weighting are based on diffusion MRI data and include the number of streamlines, FA index, and axon diameter distribution, which is measured using the recently published AxSI method. We examine local and global properties of the different resulted weighted graphs and discuss how they varied from each other. Lastly, we use each of the weighting connectomes to predict cognitive performance by using the Human Connectome Project (HCP) data set.