In cellular networks, fractional frequency reuse (FFR) is an effective inter-cell interference mitigation technique to achieve significant coverage improvement for cell edge users. Area Spectral Efficiency (ASE) is an important and vital factor to be improved in cellular networks and is defined as the number of transmitted information bits per unit area per unit time per unit bandwidth (i.e., bps/Hz/m2). In this paper, we compare ASE of different downlink FFR schemes in MIMO Heterogeneous cellular networks (MIMO HetNets), where the base station (BS) locations are modeled using Poission Point Process (PPP). Stochastic PPP is widely used in the design and analysis of signal processing algorithms especially for communication systems. ASEs are evaluated based on coverage probability functions for Strict FFR and Soft Frequency Reuse (SFR) in MIMO HetNets for both closed and open access cases. In the same time we illustrate not only the role but also the benefits of utilizing PPP in modeling the BS locations for analytical evaluation of two main types of FFR deployments. Numerical results show that, for SFR in both open and closed access cases, it is better to use MIMO HetNets than other techniques due to large interference resulted from utilizing the whole bandwidth inside the cell. Also, in SFR case, ASE is directly proportional to the power control factor βk. For Strict FFR MIMO HetNet open access case, SDMA with large numbers of antenna provides higher ASE at the expense of system complexity. For better ASE in MIMO HetNet system, it is recommended to use adaptive technique between strict FFR MIMO and MU-MIMO in terms of target threshold value of signal-to-interference ratio (SIR).