I think this is also missing the point a bit. SMT solvers are great, but as far I can it's not really SMT vs. CP or LP, they have different strengths and weaknesses. As far as the sudoku example while neat is pretty much identical in approach and expressiveness to the core.logic version I linked to.
It's true that they are similar on their expressiveness approach and at the end core.logic could have an SMT making them identical. But when we add SMT we are talking about a different beast.
For example, imagine that you want to implement a professional chess software. One romantic approach would be to find the best and nicest algorithm(s) to do that. SMT, idealistically, adds some "ugliness" trying to reach to a conclusion using every heuristic available. It's an algorithm too but it doesn't end on a good expressiveness but in inserting every heuristic available inside the resolution process.
