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The existing flare prediction primarily relies on photospheric magnetic field parameters from the entire active region (AR), such as Space-Weather HMI Activity Region Patches (SHARP) parameters. However, these parameters may not capture the details the AR evolution preceding flares. The magnetic structure within the core area of an AR is essential for predicting large solar flares. This paper utilizes the area of high photospheric free energy density (HED region) as a proxy for the AR core region. We construct two datasets: SHARP and HED datasets. The ARs contained in both datasets are identical. Furthermore, the start and end times for the same AR in both datasets are identical. We develop six models for 24-hour solar flare forecasting, utilizing SHARP and HED datasets. We then compare their categorical and probabilistic forecasting performance. Additionally, we conduct an analysis of parameter importance. The main results are as follows: (1) Among the six solar flare prediction models, the models using HED parameters outperform those using SHARP parameters in both categorical and probabilistic prediction, indicating the important role of the HED region in the flare initiation process. (2) The Transformer flare prediction model stands out significantly in True Skill Statistic (TSS) and Brier Skill Score (BSS), surpassing the other models. (3) In parameter importance analysis, the total photospheric free magnetic energy density ($\mathrm {E_{free}}$) within the HED parameters excels in both categorical and probabilistic forecasting. Similarly, among the SHARP parameters, the R_VALUE stands out as the most effective parameter for both categorical and probabilistic forecasting.