Mechanistic photosynthesis models are at the heart of terrestrial biosphere models (TBMs) simulating the daily, monthly, annual and decadal rhythms of carbon assimilation (A). These models are founded on robust mathematical hypotheses that describe how A responds to changes in light and atmospheric CO₂ concentration. Two predominant photosynthesis models are in common usage: Farquhar (FvCB) and Collatz (CBGB). However, a detailed quantitative comparison of these two models has never been undertaken. In this study, we unify the FvCB and CBGB models to a common parameter set and use novel multi-hypothesis methods (that account for both hypothesis and parameter variability) for process-level sensitivity analysis. These models represent three key biological processes: carboxylation, electron transport, triose phosphate use (TPU) and an additional model process: limiting-rate selection. Each of the four processes comprises 1-3 alternative hypotheses giving 12 possible individual models with a total of 14 parameters. To broaden inference, TBM simulations were run and novel, high-resolution photosynthesis measurements were made. We show that parameters associated with carboxylation are the most influential parameters but also reveal the surprising and marked dominance of the limiting-rate selection process (accounting for 57% of the variation in A vs. 22% for carboxylation). The limiting-rate selection assumption proposed by CBGB smooths the transition between limiting rates and always reduces A below the minimum of all potentially limiting rates, by up to 25%, effectively imposing a fourth limitation on A. Evaluation of the CBGB smoothing function in three TBMs demonstrated a reduction in global A by 4%-10%, equivalent to 50%-160% of current annual fossil fuel emissions. This analysis reveals a surprising and previously unquantified influence of a process that has been integral to many TBMs for decades, highlighting the value of multi-hypothesis methods.