Dementia is marked by a progressive decline in cognitive and emotional capacities, presenting significant challenges to daily functioning. This includes prominent neurodegenerative disorders like Alzheimer's disease (AD) and Frontotemporal dementia (FTD). Recent advancements in electroencephalogram (EEG) sensors and processing tools, project it as a potential biomarker for detecting neuronal and cognitive changes associated with various dementia types. Investigations related to characterization and differentiation are yet to be explored for range identification and assigning quantitative values to resting state EEGs from different dementia conditions. In this study, two features that capture the band-specific alterations are computed for each subject. These attributes formed the basis of the Dementia Severity Index (DSI), a threshold-based methodology designed to categorize individuals into AD, FTD, and HC from the resting EEG. The introduced thresholding technique underwent validation using machine learning methodologies, specifically the k-nearest neighbors algorithm (kNN) and random forest (RF), achieving accuracies of 81.6% and 81.37%, respectively. The classification outcomes of derived DSI from F1 and F2 are compared. The $DSI$ corresponding to significant feature F1 is validated on two diverse EEG datasets. The study aims to contribute to the field by providing a set of dementia indexes capable of distinguishing between AD and FTD-based dementia and discriminating against HC. Additionally, the ability of significant features to reflect cognitive performance is explored using the Spearman correlation coefficient (r) to quantify the relationship between predicted Mini-Mental State Examination (MMSE) and actual MMSE scores. The study also delves into the variations in sensor and source domain classification using features F1 and F2. The findings of the proposed approach hold promise for capturing a range of values that can effectively classify AD, FTD, and HC, while also offering the advantage of computationally efficient classification when compared with the existing subjective assessment.