Tests to find which theory agrees better with observation
I'm not sure about the best statistical way, but one practical approach would be to compare actuals v expected for each of the two hypothetical curves.

Calculating the sum of squared differences (i.e. sum((y_obs - y_theory)^2)) will give you a numerical estimate of goodness-of-fit for each curve. You could also use other metrics depending on your application (e.g. RMSE, RMSLE, SMAPE...).

Or, for each theoretical curve, you could look at the distribution of differences between the actual observation and the value predicted by the curve. It can be handy to view these empirical differences graphically.

I'm sure there are other statistical ways to evaluate goodness-of-fit.