Solid-state transformer (SST) and hybrid transformer (HT) are promising alternatives to the line-frequency transformer (LFT) in smart grids. The SST features medium-frequency isolation, full controllability for voltage regulation, reactive power compensation, and the capability of battery energy storage system (BESS) integration with multiport configuration. The HT has a partially rated converter for fractional controllability and can integrate a small BESS. Fast grid-edge voltage fluctuations from increased solar photovoltaic (PV) and electric vehicle (EV) penetration are difficult to manage for mechanical load tap changers. Hence, along with the trend toward more BESS in the grid, the controllability and the storage-integration capability of the SST and HT are of strong interest. However, a review of literature shows existing SST and HT research is mostly at converter level, while system-level assessments are scarce. Assessing technical and economic impacts is critical to understanding the benefits and role of the SST and HT to guide future research, which is presented for the first time in this article. Experimental results from medium-voltage (MV) SST and MV HT prototypes are shown to confirm equipment-level feasibility, where the voltage controllability waveforms of an MV HT prototype are reported for the first time. Comparative simulations are performed on a modified IEEE 34-bus system. A grid-model-less decentralized grid-edge voltage control method and a day-ahead BESS dispatch method are proposed for the SST and HT. The simulations show that the SST and HT with integrated storage can host more PV, achieve peak shaving, mitigate voltage fluctuation and reverse power flow, and support energy arbitrage for operational cost reduction, compared to the LFT. Moreover, comprehensive analyses of net present value (NPV) and internal rate of return (IRR) are performed under different installed PV capacities, HT’s partial converter ratings, and BESS capacities. Sensitivities to future cost reductions of the PV and BESS are studied. Although the NPV and IRR are currently negative, 60% capital cost reduction or 150% revenue increase will make the SST and HT economically viable in the use case studied.