Not easy to compare as each one is dedicated to different applications.
PHREEQC is widely popular among the geochemical modeling community and is considered by far the most complete geochemical modeling package. It is very flexible and easy to use. In version 3, there is support for modeling high-pressure-temperature systems.
TOUGHREACT couples a geochemical engine (REACT) with the well-known multiphase and multicomponent TOUGH2 code (developed by LBNL) which has well-known applications in geothermal reservoir engineering and CO2 storage applications.
The code REACT has fewer capabilities for pure geochemical modeling compared to PHREEQC, and to my best knowledge, it is not (or much less) maintained than PHREEQC. Hence, the latter is better for pure geochemical models or 1D fully saturated reactive transport simulations.
TOUGHREACT is advised for multi-dimensional (2D or 3D) reactive transport applications possibly with multiphase fluid flow and transport.