Choosing which interest rate model to go with?

Calibrate to many observed curves, over all kinds of shapes: flat, normal, inverted, and humped, and measure and compare the model fitting errors. If you can't find all the shapes in history, make them up as possible scenarios (stresses).

Classical Vasicek and CIR are parsimonious (have few parameters), so not very good at properly matching today's full observed curve. But what could be more dramatic is that one of them may fail to calibrate altogether (say maybe to an inverted curve, maybe stressed a bit).

(Note: the competition is a bit unfair, given that CIR cannot accommodate negative interest rates observed these days.)

One more note, given a set of model parameters, you can generate curves at future times (formulas for zero-coupon bond prices, $P(t,T)$, are valid for all $tgeq 0$, not just $t=0$, and all $T geq t$). This exercise (somewhat complementary to the calibration test) shows the capacity of the model to generate a reasonable variety of curve shapes at future times.