Comparison of behaviors and performances between large amplitude nonlinear direct and parametric shunted piezoelectric energy harvesters (PEH) are addressed in this paper. A model of geometrically exact piezoelectric laminated beam with parametric excitation is proposed and simplified with Euler-Bernoulli and inextensible assumptions, Taylor series expansion of transverse displacement and truncation, and first-mode Galerkin expansion. A cantilever beam with two collocated patches is then considered and patches placement and geometry are computed based on coupling-factor optimization. Analytical and numerical resolution methods are compared. PEH behaviors and performances are compared regarding the dissipated power in the resistor at resonance. Three cases are considered: linear-direct, nonlinear-direct and nonlinear-parametric. Results show a gap between direct and parametric PEH performances and the importance of the threshold excitation parametric effect.