Shape Memory Alloys (SMAs) exhibit the ability to undergo large deformations but can recover permanent strains via heating (shape memory effect) or when stress is removed (superelastic effect). This study evaluates the comparative seismic performance of steel moment resisting frames (SMRFs) with innovative beam-to-column connections that use SMA bars as connecting elements. The performance evaluation studies are based on two types of SMA beam-to-column connections: (1) superelastic SMA connections with recentering capability; (2) martensitic SMA connections with high energy dissipation capacity. Fiber models for these SMA connections are implemented in the OpenSees finite element framework, and are verified against data from full-scale experimental tests that were performed on a prototype SMA connection in previous research at Georgia Tech. Three- and a nine-story model buildings with partially-restrained (PR) moment frames are selected from the SAC Phase II Project as case studies. Non-linear time history analyses on these model buildings, with and without SMA connections, are conducted using suites of ground acceleration records from the SAC Phase II project that represent different seismic hazard levels. Several SMA connections are designed for each structure, and their effect on peak and residual inter-story drift angles, connection rotations, and normalized dissipated hysteretic energy demands are investigated to determine the most suitable design. Finally, the seismic demands on the model buildings with conventional PR and selected SMA connections are evaluated in a probabilistic framework. The resulting seismic demand relationships are used to assess the effectiveness of the SMA connections in enhancing the building performance over a range of demand levels. The results of this performance evaluation show that the SMA connections are most effective in controlling structural response under high levels of seismic intensity leading to large deformation demands. In particular, the energy dissipating SMA connections are found to be effective in reducing maximum deformation demands, while the recentering SMA connections are more suitable for controlling residual deformations in the structure.