Propagation power really depends on the problem. For some problems, propagation is amazingly good, and for some it does not do much at all.
One can characterize propagation algorithms for the amount of propagation they do. A domain consistent propagation algorithm will make all deductions that are possible to make in a certain state, removing all values for variables that are not a part of any solution to that constraint. Loosely, a bounds consistent propagation algorithm will do the same, but only for the bounds of the variables.
The constraint used in Sudoku (called all_different or distinct) has really good propagation algorithms (both bounds and domain consistent), and is one of the cornerstones of constraint programming.
One can characterize propagation algorithms for the amount of propagation they do. A domain consistent propagation algorithm will make all deductions that are possible to make in a certain state, removing all values for variables that are not a part of any solution to that constraint. Loosely, a bounds consistent propagation algorithm will do the same, but only for the bounds of the variables.
The constraint used in Sudoku (called all_different or distinct) has really good propagation algorithms (both bounds and domain consistent), and is one of the cornerstones of constraint programming.