Comparing the sizes of two search spaces by comparing their numbers of possibilities I am trying to solve an optimisation problem and come up with two Integer Linear Programming models. For each model, I am able to find a function that calculate the number of possibilities based on different variables, e.g. problem sizes.

I cannot directly conclude that one model has a smaller search space than the other. Instead, I develop an application that compares the actual numbers of possibilities between 2 models based on different values of the variables.

My application tries millions of different variables and shows that the number of possibilities of one model is less than the other 99% of the time. Is it enough to conclude that it is likely for one model to have the smaller search space, and to be solved faster than the other?
There is no easy way to predict which ILP model will be faster to solve.  Counting the number of variables is not a reliable predictor.  Estimating the size of the "search space" (the number of feasible solutions) is not a reliable predictor.  There is, in general, no fully reliable way to tell which model will be faster -- short of actually trying both.

Instead, my recommendation is that you try experiments.  Try solving both models, and see which takes longer to solve.  If your problem is parameterized in size, you can try solving for smaller sizes and see if a pattern emerges.