Which model is right? and which one is wrong? This goes back to the issue of overfitting, a model with too few parameters won't fit the data well, too many and it will but the confidence intervals will be wide. If the goal of the model is to predict future values, a model with too many parameters won't do it well, and if the goal is to interpret values scientifically, the CIs will be too big. And finally as something that is only tangentially related to fitting models:
Sources: Census data polynomial curve fitting, Mexican Turkeys, Doge, and Motulsky.