As the technical trends for the next-generation wireless network significantly extend the near-field region, a performance reevaluation of integrated sensing and communications (ISAC) with an appropriate channel model to account for the effects introduced by the near field becomes essential. In this paper, a near-field ISAC framework is proposed for both downlink and uplink scenarios based on an accurate channel model. A uniform planar array is equipped at a base station, where the impacts of the effective aperture and polarization of antennas are considered. For the downlink case, three distinct designs are studied: a communications-centric (C-C) design, a sensing-centric (S-C) design, and a Pareto optimal design. Regarding the uplink case, the C-C design, the S-C design and a time-sharing strategy are considered. Within each design, sensing rates (SRs) and communication rates (CRs) are derived. To gain further insights, high signal-to-noise ratio slopes and rate scaling laws concerning the number of antennas are examined. The attainable near-field SR-CR regions of ISAC and the baseline frequency-division S&C are also characterized. Numerical results reveal that, as the number of antennas in the array grows, the SRs and CRs under our accurate model converge to finite values, while those under conventional far- and near-field models exhibit unbounded growth, highlighting the importance of precisely modeling the channels for near-field ISAC.