In this work, we conduct comprehensive comparisons between four variants of independent component analysis (ICA) methods and three variants of sparse dictionary learning (SDL) methods, both at the subject-level, by using synthesized fMRI data with ground-truth. Our results showed that ICA methods perform very well and slightly better than SDL methods when functional networks' spatial overlaps are minor, but ICA methods have difficulty in differentiating functional networks with moderate or significant spatial overlaps. In contrast, the SDL algorithms perform consistently well no matter how functional networks spatially overlap, and importantly, SDL methods are significantly better than ICA methods when spatial overlaps between networks are moderate or severe. This work offers empirical better understanding of ICA and SDL algorithms in inferring functional networks from fMRI data and provides new guidelines and caveats when constructing and interpreting functional networks in the era of fMRI-based connectomics.