The Cluster-Span Threshold (CST) is a recently introduced unbiased threshold for functional connectivity networks. This binarisation technique offers a natural trade-off of sparsity and density of information by balancing the ratio of closed to open triples in the network topology. Here we present findings comparing it with the Union of Shortest Paths (USP), another recently proposed objective method. We analyse standard network metrics of binarised networks for sensitivity to clinical Alzheimer's disease in the Beta band of Electroencephalogram activity. We find that the CST outperforms the USP, as well as subjective thresholds based on fixing the network density, as a sensitive threshold for distinguishing differences in the functional connectivity between Alzheimer's disease patients and control. This study provides the first evidence of the usefulness of the CST for clinical research purposes.