The discovery of lead-free piezoelectric materials is crucial for future information and energy storage applications. Enhanced piezoelectric and other physical properties are commonly observed near the morphotropic phase boundary (MPB) composition of ferroelectric solid solutions. The $(1\ensuremath{-}x)\mathrm{Ba}({\mathrm{Zr}}_{0.2}{\mathrm{Ti}}_{0.8}){\mathrm{O}}_{3}\text{\ensuremath{-}}x({\mathrm{Ba}}_{0.7}{\mathrm{Ca}}_{0.3}){\mathrm{TiO}}_{3}$ $(\mathrm{BZT}\text{\ensuremath{-}}x\mathrm{BCT})$ system exhibits a large electromechanical response around its MPB region at $x=0.5$. We report experimental and theoretical results of $\mathrm{BZT}\text{\ensuremath{-}}x\mathrm{BCT}$ over a wide composition range $(0.3\ensuremath{\le}x\ensuremath{\le}1.0)$. X-ray diffraction and Raman spectroscopy studies indicate a composition-induced structural phase transition from a rhombohedral $(R3m)$ phase at $x\ensuremath{\le}0.4$ to a tetragonal $(P4mm)$ phase at $x\ensuremath{\ge}0.6$ through a multiphase coexistence region at 0.45 \ensuremath{\le} $x\ensuremath{\le}0.55$ involving orthorhombic + tetragonal (Amm2 + $P4mm$) phases. First-principles calculations elucidate the phase competition in the coexistence region. The critical composition $(x=0.5)$ displays enhanced dielectric, ferroelectric, and piezoelectric properties, where notably ${d}_{33}\ensuremath{\sim}320$ pC/N. This paper provides clear evidence of Amm2 + $P4mm$ crystallographic phases in the MPB region, which is responsible for the improved functional properties.