Constraint Programming is NP-complete (non-polynomial bounds, likely exponential complexity).

Simplex is provably within the polynomial bounds of complexity, ie: simplex is a so called "easy" problem in complexity theory.

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You're right that simplex is applied to optimization problems. Constraint programming could be seen as a "more generic" optimizer, in that it can handle integer-optimization (simplex cannot handle integer optimization at all).

Of course, integer-optimization is NP complete, which means that constraint programming is innately "inefficient" or "hard" in terms of complexity.