Comparing the sizes of two search spaces by comparing their numbers of possibilities
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.